In the problem 4 conditions are given using those conditions have to perform stack operations.
Check options one by one and which one is violating above conditions.
Let me start from first
1) Top(push(push($\epsilon$,X),Y)):
It can be rewritten as $Top(push(s,Y))$=Y. using rule 4 with rule 2 [Here s=push($\epsilon ,X$)]
2)pop(push($\epsilon ,X$))=$\epsilon$ . using rule 3.
3)push(pop(push($\epsilon$,X)),Y):
it can be rewritten as push($\epsilon$,Y) it is a stack. using rule 2 with rule 3.
4) Pop(pop(push($\epsilon$,X))) =X .
It can be rewritten as ${\color{Red} p}{\color{Red} o}{\color{Red} p}{\color{Red} ({\color{Red} \epsilon }}{\color{Red} )}$ !=X.
using rule 3.
Hence answer should be 4.
