$(4$ pts$.)$ Fig. $2$ shows a switching network $($stack$)$ for train carts with stack size $2($where only two carts, say A and $B$ as shown, could be pushed into the stack$).$ Each cart in the left side should be pushed into the stack once and popped out once to the right side. List all possible permutations $($in the right$)$ of the four carts, which are in the left initially and named as $A,B,C$ and $D$ from right to left.

$6/6$

$6$

Fig. $2$ Switching network for train carts with stack size $2$