"The young student is waiting beside the buses."
Translation:A fiatal diák a buszok mellett vár.
Your sentence is fine, and should be accepted. It does have a different emphasis than the given translation, but it is impossible to tell from the English prompt which one is required. The difference between the two is clearest if you think of them as answers to questions:
Hol vár a fiatal diák? A fiatal diák a buszok mellett vár.
Ki vár a buszok mellett? A fiatal diák vár a buszok mellett.
Notice that the word (or phrase) immediately preceding the verb in the answer matches the question word immediately before the verb in the question. ("Hol? A buszok mellett." versus "Ki? A fiatal diák.")
So your sentence emphasizes who is waiting, whereas the given translation emphasizes where the young student is waiting.
Mellett is a postposition, meaning it has to come immediately after the thing it modifies. So:
a buszok mellet means "beside the buses", whereas
a fiatal diák mellet means "beside the young student"
This sentence really has three parts: a fiatal diák ("the young student") as its subject, a buszok mellett ("beside the buses") and the verb, vár. The three parts can be put in various orders, but the word order within each part is grammatically fixed and can't be changed.
To explain a bit more, your sentence A fiatal diák mellett a buszokat vár is almost grammatical, but with a different meaning. I would parse it in three parts as follows:
A fiatal diák mellett - beside the young student (a location phrase)
a buszokat - the buses; with the accusative -t ending, it must be the object of some transitive verb, and sure enough
vár is the verb, in its 3rd person singular form. This doesn't quite work, though, because of the definite object a buszokat in this sentence; the conjugation would need to be the definite form, várja.
So the subject in this sentence must be understood to be "he" or "she" even though it is omitted from the sentence. All together, the meaning of A fiatal diák mellett a buszokat várja would be "He waits for the buses next to the young student."