The computer first runs $\texttt{x = [2, 4, 8]}$. This tells the computer to take $\tt x$ and point it to the array, so we get the following picture:

Next, the computer runs $\texttt{y = x}$. It takes $\tt y$ and points it wherever $\tt x$ points.

Next, the computer runs $\texttt{x[0] = 1}$. It takes $\texttt{x[0]}$ and points it to the number 1.

Finally, the computer runs $\texttt{print(y[0])}$. The computer steps to the $\tt y$, and then along the $\tt 0$ pointer, and prints out $\tt 1$.

This result might have been surprising, since we changed $\tt x[0]$, and then $\tt y[0]$ also changed at the same time. But it's clear why this happened if you understand how pointers work in Python.