Final answer:
The group of words 'studying for tests' is an adjective phrase because it lacks a subject of its own and functions to describe the noun 'people' in the sentence. Option number a is correct.
Step-by-step explanation:
In the sentence "At school he saw many people studying for tests," the group of words you are asking about is an adjective phrase.
A clause will have both a subject and a verb, but the phrase "studying for tests" lacks a subject of its own, which means it does not contain both elements required to form a clause. Instead, this phrase functions as a unit within the sentence to describe the people, telling us what they were doing, which is characteristic of an adjective phrase.