Probably the hint wasn't completely accurate then.

Your sentence needs a verb, which in this case is 걸리다 (here in it's conjugated 요 form).

동안 : during

얼마나 : how much

얼마나 ≒ 얼마 동안

In this case, it's either ~나 or -동안. They cannot be used along with each other.

얼마 is a noun it takes particles and is acted on as such
저는 얼마를 모른다 i dont know how much
삼천 원은 얼마이다 three thousand won is how much

얼마나 is an adverb and can describe verbs, adjectives, other adverbs.
그걸 하려고 얼마나 걸러니? how long does it take to do that?
얼마나 많은 사과가 있니? how many apples do you have?
그녀가 얼마나 열심히 연습했니? how hard did she practice?

its explained a bit more here