"What don't we have?"
Translation:Чего у нас нет?
When you say you don't have something you use the genitive case instead of nominative, so you say у меня нет книги (genitive singular) for "I don't have the/a book" or у меня нет книг (genitive plural) for "I don't have (the/any) books" even though the word for book is книга.
Now when you ask a question что also needs to be inflected and it has to match the case of the answer.
что это? (nom)
это книга (nom)
чего у нас нет? (gen)
у нас нет книги (gen)
That works, or just "что у нас?"
The longer version is probably appropriate for more situations. Unfortunately I can only come up with vague intuition about when I would use one form versus the other. :(
у is a preposition. The word it operates on directly follows it, which in this case is нас, so it has to directly follow у.
The question word usually goes at the beginning of the sentence in Russian. To figure out the case and how to order the words, try this:
If you are asking a question like the one above, imagine what an answer might look like: «у нас нет воды»
Next, switch the question word in for whichever word is the one that answers it. In this case we are asking "what", and the answer is "water". Make sure you use the same case of the question word as the answer word: «у нас нет чего»
Lastly, move the question word to the beginning: «чего у нас нет?»
It works in many cases.