Answer:
The correct usage of the future perfect tense is found in option c) "She will have left for the airport when you arrive."
The future perfect tense is used to express an action that will be completed before a future point in time. In this sentence, the action of "leaving for the airport" will be completed before the future action of "you arrive."
Option b) "They had painted the house before the party" is in the past perfect tense, indicating an action that was completed before a past point in time.
Option a) "I have finished my homework tomorrow" is incorrect because the word "tomorrow" refers to a future point in time, and we cannot use future tense to refer to an action that has already occurred.
Option d) "We will have went on vacation next month" is incorrect because "went" is the past tense form of the verb "go." The correct form is "We will have gone on vacation next month" to express an action that will be completed before a future point in time.