Explanation:
To understand why the correct answer is "will have been going," we need to analyze the sentence structure and the timeline of the action.

Sentence Structure:
The sentence is in the future tense and expresses an action that will be completed before a specific time in the future.

Timeline:
The action of going home will occur before the next week. This means that by the time the next week arrives, the action will already be completed.

Verb Tenses:
To express this idea, we need to use the future perfect continuous tense, which is formed by combining "will have been" with the present participle form of the verb.

Breakdown of the Correct Answer:

The correct answer is "will have been going," which consists of three parts:

1. Will: The auxiliary verb "will" indicates the future tense and shows that the action will happen in the future.

2. Have been: The helping verb "have been" is the future perfect continuous form of the verb "be." It indicates that the action has been ongoing and will continue until a specific point in the future.

3. Going: The present participle form of the verb "go" is used to indicate the action of going home.

Putting it Together:

By combining these three parts, we get "will have been going," which accurately expresses the idea that the action of going home will be ongoing and will continue until the specified time in the future (next week).

Example:
To further illustrate the usage of "will have been going," consider the following sentence:

"We will have been going home for five weeks by the time we return."

In this example, the action of going home will have been ongoing for five weeks by the time the individuals return. It emphasizes the continuous nature of the action leading up to a specific point in the future.