archive-faqs.php

<?php
$categories = get_terms('faq_cat'); ?>
<ul class="cat-list">
  <li><a class="cat-list_item active" href="#!" data-slug="">All FAQS</a></li>
  <?php foreach($categories as $category) : ?>
    <li>
      <a class="cat-list_item" href="#!" data-slug="<?= $category->slug; ?>">
        <?= $category->name; ?>
      </a>
    </li>
  <?php endforeach; ?>
</ul>

<?php
  $faqs = new WP_Query([
   'post_type' => 'faqs',
    'posts_per_page' => -1,
    'order_by' => 'date',
    'order' => 'desc',
]);
?>

<?php if($faqs->have_posts()): ?>
  <ul class="project-tiles">
    <?php
      while($faqs->have_posts()) : $faqs->the_post();
        the_title();
      endwhile;
    ?>
  </ul>
  <?php wp_reset_postdata(); ?>
<?php endif; ?>

<script>
  jQuery(document).ready(function($) {
    $('.cat-list_item').on('click', function() {
  $('.cat-list_item').removeClass('active');
  $(this).addClass('active');

  $.ajax({
    type: 'POST',
    url: '/wp-admin/admin-ajax.php',
    dataType: 'html',
    data: {
      action: 'filter_projects',
      category: $(this).data('slug'),
    },
    success: function(res) {
      $('.project-tiles').html(res);
    }
  })
});
});
</script>