"What would you like to eat?"
Translation:Was möchtet ihr essen?
Möchten is unusual. It is actually the subjunctive form of "mögen", which is why it has the same ending system as subjunctive and past tense verbs. If you remember that mögen translates to "like" in English, it makes perfect sense that its subjunctive möchten means "would like to".
We say that in Germany (at least where I come from), but grammatically it is a strange structure... I don't know whether the Duden accepts it as grammatically correct or not.
You could also say 'etwas zu essen/Essen', 'ich habe etwas zu essen/Essen, and the same with 'zu trinken/Trinken'.
The funniest is 'das Zu-Essen / das Zu-Trinken'. :D (meaning 'das Essen, das Getränk')
Well, I think they are usable in spoken language, but not in written. So you are not wrong, you were just taught a colloquial structure that probably will be understood. ;)