"what do you answer?" is wrong. suppose you can say "what is your answer?".

An alternative answer is, "how do you answer (this)?", however Rinoa's response is probably the better one. I think the question sounds wrong because "what" indicates a noun, and the possessive 'your' indicates that "answer" is a noun and not a verb. It's still a possible sentence in English, but it sounds clumsy because 'answer' can be a verb or a noun. It's better to make it clear by saying "how do you answer (=verb)" or what is your answer (=noun)"