Once they told me to use one stack for enqueueing and one for dequeueing, I immediately solved the problem. What I didn't understand is why you would a.) implement your own queue structure and b.) implement it in such a non-intuitive way.

Now that I know this would be for a functional language, it makes way more sense. At the time I couldn't get over why you wouldn't just use a doubly-linked list like the standard implementation in most OO languages.