Queue implemented using stacks
I believe the question is asking you to implement the queue so that every time you perform a queue operation (enqueue or dequeue) your implementation does O(1) total operations on the stacks used to implement this. For example, an implementation that performed at most 137 total pushes and pops per time that the client calls enqueue or dequeue would satisfy this requirement, but an implementation that requires, say, $n$ stack operations per enqueue would not meet this requirement.