English has a class of verbs called "linking verbs," such as "to be," "to appear," "to seem," "to sound," etc. These linking verbs do not take an adverb, and merely link the subject to an adjective. For example: The house IS large. (NOT the house is largely) The house appears large (NOT the house appears largely) The house seems large (NOT the house seems largely) And, your example, the answer sounds correct. (NOT the answer sounds correctly). In other words, "correct" modifies "answer" rather than the verb "to sound" because this verb is considered a "linking verb" in English.

Because "answer" is a noun here, and needs an adjective. "Correct" is the adjective form.