Which question is grammatically correct: “does he like” or “does he likes”?

The correct one is “Does he like?” This is a question in present simple tense. We form questions with the help of the auxiliary verbs do and does and the base form(infinitive) of the main verb. A base form (infinitive) is a verb without any suffixes. We use do with I, you, we and they. We use does with he, she and it.

You can read more about present simple questions and do a quiz here.