FULL CODE CAROUSEL

import 'package:flutter/material.dart';
import 'package:flutter/animation.dart';

class Intro extends StatefulWidget {
  @override
  _IntroState createState() => _IntroState();
}

class _IntroState extends State<Intro> with TickerProviderStateMixin {
  Animation animation, fadeout;
  AnimationController animationController, fadeController;
  PageController controller;

  int carouselIndex, itemIndex;

  @override
  void initState() {
    super.initState();
    controller = PageController(
      initialPage: 0,
      keepPage: true,
      viewportFraction: 0.8,
    );

    animationController = AnimationController(
      duration: Duration(seconds: 2),
      vsync: this,
    );
    fadeController = AnimationController(
      duration: Duration(seconds: 7),
      vsync: this,
    );

    fadeout = Tween(begin: -1.0, end: 0.0)
        .animate(CurvedAnimation(parent: fadeController, curve: Curves.easeIn));
    fadeController.forward();

    animation = Tween(begin: -1.0, end: 0.0).animate(CurvedAnimation(
        parent: animationController, curve: Curves.fastOutSlowIn));
    animationController.forward();
  }

  @override
  Widget build(BuildContext context) {
    final double width = MediaQuery.of(context).size.width;

    return AnimatedBuilder(
        animation: animationController,
        builder: (BuildContext context, Widget child) {
          return Scaffold(
              appBar: new AppBar(
                backgroundColor: Colors.white,
                elevation: 2.0,
                leading: IconButton(
                    icon: Icon(
                      Icons.list,
                      color: Colors.red,
                    ),
                    onPressed: () {
                      Navigator.pop(context);
                    }),
              ),
              body: ListView(children: <Widget>[
                new Stack(
                  children: <Widget>[
                    new AspectRatio(
                      aspectRatio: 10 / 100,
                      child: new Container(
                        decoration: BoxDecoration(
                            image: DecorationImage(
                                image: AssetImage('assets/dashboard.png'),
                                alignment: Alignment.topCenter)),
                      ),
                    ),
                    new Transform(
                      transform: Matrix4.translationValues(
                        animation.value * width,
                        0.0,
                        0.0,
                      ),
                      child: Padding(
                        padding: const EdgeInsets.symmetric(horizontal: 12.0),
                        child: Container(
                          child: Column(
                            children: <Widget>[
                              SizedBox(height: 60.0),
                              new Row(
                                children: <Widget>[
                                  Expanded(
                                      child: Column(
                                    mainAxisAlignment: MainAxisAlignment.start,
                                    crossAxisAlignment:
                                        CrossAxisAlignment.start,
                                    children: <Widget>[
                                      Text(
                                        'Have you',
                                        style: TextStyle(
                                            color: Colors.black,
                                            fontSize: 24.0,
                                            height: 0.1),
                                      ),
                                      Padding(
                                        padding:
                                            const EdgeInsets.only(left: 8.0),
                                        child: Text(
                                          'subscribe',
                                          style: TextStyle(
                                              color: Color(0xFFFFB300),
                                              fontSize: 24.0,
                                              height: 0.9),
                                        ),
                                      ),
                                      Padding(
                                        padding:
                                            const EdgeInsets.only(left: 13.0),
                                        child: Text(
                                          'PewDiePie?',
                                          style: TextStyle(
                                              color: Color(0xFFFF1744),
                                              fontSize: 24.0,
                                              height: 0.8),
                                        ),
                                      )
                                    ],
                                  )),
                                ],
                              ),
                              SizedBox(height: 7.7),
                            ],
                          ),
                        ),
                      ),
                    ),
                    new FadeTransition(
                      opacity: fadeController
                          .drive(CurveTween(curve: Curves.easeIn)),
                      child: new Padding(
                        padding: const EdgeInsets.symmetric(
                            horizontal: 22.0, vertical: 115.0),
                        child: new Row(
                          children: <Widget>[
                            Expanded(
                              child: Row(
                                children: <Widget>[
                                  new Padding(
                                    padding: const EdgeInsets.only(right: 3.3),
                                    child: new Container(
                                      height: 40.0,
                                      width: 65.0,
                                      decoration: BoxDecoration(
                                        color: Colors.red,
                                        borderRadius:
                                            BorderRadius.circular(5.0),
                                      ),
                                      child: Column(
                                        mainAxisAlignment:
                                            MainAxisAlignment.center,
                                        children: <Widget>[
                                          Text('yes',
                                              style: TextStyle(
                                                  color: Colors.white,
                                                  fontSize: 21.5))
                                        ],
                                      ),
                                    ),
                                  ),
                                  new Padding(
                                    padding: const EdgeInsets.only(left: 3.3),
                                    child: new Container(
                                      height: 40.0,
                                      width: 65.0,
                                      decoration: BoxDecoration(
                                        color: Colors.greenAccent,
                                        borderRadius:
                                            BorderRadius.circular(5.0),
                                      ),
                                      child: Column(
                                        mainAxisAlignment:
                                            MainAxisAlignment.center,
                                        children: <Widget>[
                                          Text('no',
                                              style: TextStyle(
                                                  color: Colors.white,
                                                  fontSize: 21.5))
                                        ],
                                      ),
                                    ),
                                  )
                                ],
                              ),
                            )
                          ],
                        ),
                      ),
                    ),
                    //HORIZONTAL LISTVIEW
                    new ListView.builder(
                      itemCount: 3,
                      scrollDirection: Axis.horizontal,
                      padding: EdgeInsets.symmetric(vertical: 16.0),
                      itemBuilder: (BuildContext context, int index) {
                        if (index % 3 == 0) {
                          return _buildCarousel(context, index ~/ 3);
                        } else {
                          return Divider();
                        }
                      },
                    ),
                  ],
                ),
              ]));
        });
  }

  Widget _buildCarousel(BuildContext context, int carouselIndex) {
    return Column(
      mainAxisSize: MainAxisSize.min,
      children: <Widget>[
        Text('Carousel $carouselIndex'),
        SizedBox(
          // you may want to use an aspect ratio here for tablet support
          height: 200.0,
          child: PageView.builder(
            // store this controller in a State to save the carousel scroll position
            controller: PageController(viewportFraction: 0.8),
            itemBuilder: (BuildContext context, int itemIndex) {
              return _buildCarouselItem(context, carouselIndex, itemIndex);
            },
          ),
        )
      ],
    );
  }

  Widget _buildCarouselItem(
      BuildContext context, int carouselIndex, int itemIndex) {
    return Padding(
      padding: EdgeInsets.symmetric(horizontal: 4.0),
      child: Container(
        decoration: BoxDecoration(
          color: Colors.grey,
          borderRadius: BorderRadius.all(Radius.circular(4.0)),
        ),
      ),
    );
  }
}