from tkinter import *
from random import randint

root = Tk()

field = [[None] * 4 for i in range(4)]

def add_tile(event):
    i = randint(0,3)
    j = randint(0,3)
    if not field[i][j]:
        field[i][j] = Label(root, text = "2", font = "Arial 48", bg="lightblue")
        field[i][j].grid(row = i, column = j)
    else:
        add_tile(event)

root.bind("<Left>", add_tile)

root.mainloop()


[None, None, None, None]
[None, None, None, None]
[None, None, None, None]
[None, None, None, None]