Remember that "fare" can mean "make" as well, so a bad translation of "fare domande" would be "to make questions" -- a more natural translation, "to ask questions". Thus:
Loro non fanno neanche delle domande.
Here's a super-bad, super-literal transliteration:
They not make even some questions.
Now, to improve it, how would we express it in more natural English?
They don't even ask (any) questions.
Yes! And once you know that, the rest of the sentence falls into place, if you think about it. Good sentence duolingo!
Here's help for all of us on the verb fare ...