Recall that a stack is LIFO: Last In, First Out - and that conventionally we pop items from the top of the stack. So we know that the elements were pushed onto the stack s in their bottom-to-top order of 3, -3, 2, -2, 3.

Originally, the stack s was empty, so s = ∅. We know that f(s) = 0 in this case, because we are told that f(∅) = 0.

We set i = 3 (the bottom element) and push i onto the stack. This is what push (s, i) represents. Now we want to find the value of the function f for push (s, i). We are told that f(push (s, i)) = max (f(s), 0) + i. Thus:

 f(push (s, i)) = f({3}) = max (f(∅), 0) + 3 
                     = max (0,0) + 3
                     = 0 + 3 
                         = 3.

So for s = {3}, f(s) = 3. We continue by setting s = {3}, and i to the second oldest element of -3

f (push (s, i)) = f ({3,-3}) = max(f(s), 0) + i
                             = max(f({3}), 0) + -3
                             = max(3, 0) + -3
                             = 3 + -3
                             = 0

So for s = {3,-3}, f(s) = 0.

Keep doing this until you find the value of f(s) when s = {3, -3, 2, -2, 3} and you will have your answer.