"More loudly" vs "louder". Correct usage
They are both well-formed and idiomatic sentences. Whoever insisted on that quiz answer alone is trying to specify a very particular standard, where modifiers of verbs must outwardly look like an adverb (using '-ly'). But that is not the case as 'louder' works as an adverb, too.
Both; louder and more loudly are the same as loud is also an adverb not always an adjective. Example: Can you speak louder, please? in this case 'louder' modifies 'speak.'