The verb which correctly completes the sentence is the following one:
c) marches.
An army of ants marches quickly across the sand.
In the sentence, the subject is "an army of ants", that is, a single army, therefore singular. Since the sentence is in simple present tense and is affirmative, as well as the subject is in third person singular (an army of ants marches= it marches), the rule of adding "s", "ies", or "es" to the verb applies. Since the main verb ends in "ch", "es" must be added to it.