Correct answer is A) give.
Sentences that are grammatically correct have subject verb agreement, and the subject or noun component of the sentence drives the verb that is used. The tricky part of this sentence is the prepositional phrase "of sugar" that is right before the verb. Some will identify sugar as the noun and then go on to choose the incorrect verb based on this choice. Sugar is the object of the prepositional phrase however. The noun or subject of the sentence is LEVELS which is a plural. In the English language, plural subjects are paired with singular verbs almost always. Singular subjects are paired with plural verbs as well. But the key strategy here is to get the "extra" words out of the way and look only at what's necessary.
If you look at the sentence with just the subject and verb/predicate, the answer is obvious. Look at the following:
High levels of sugar gives some people a headache. Easy to tell this is not correct just by reading it. High levels of sugar give some people a headache. Easy to tell this IS correct as the subject and predicate match.