You will require two queue if you want production grade solution, and can e achieve in two ways:
Method 1:
push operation of the Stack
: enqueue in queue1
pop operation of the Stack
: while size of queue1 is bigger than 1, pipe dequeued items from queue1 into queue2; dequeue and return the last item of queue1, then switch the names of queue1 and queue2
Method 2:
push operation of the Stack
: enqueue in queue2; enqueue all items of queue1 in queue2, then switch the names of queue1 and queue2
pop operation of the Stack
: deqeue from queue1