Question

people have held athletic competitions since the time of the ancient greeks.
have held
athletic competitions
held athletic
people have

Explanation:

The task is to identify the complete predicate of the sentence "People have held athletic competitions since the time of the ancient Greeks." The complete predicate includes the verb phrase and all words that describe the action. "have held" is the verb phrase, and "athletic competitions" along with the prepositional phrase (not in the options) form the rest of the predicate; among the given options, "have held athletic competitions" is the full core predicate part.

Answer:

have held athletic competitions