Answer: A. Have been destroyed
Step-by-step explanation:
The following statement: Many lives __________ by drug and alcohol abuse. Is written in the past tense. And therefore the only acceptable answer(s) are the ones referring to something that had already happened.
The two answers that follow this category are "have been destroyed" and "been destroyed" while both representing past tense, the latter is grammatically when associated with the respective context.
As a result of our reasoning, we later find that the answer is Many lives have been destroyed by drug and alcohol abuse.