Explanation:

To understand why the correct answer is "shall have finished," let's break down the sentence and the different verb tenses used.

1. Simple Present Tense:
The sentence starts with "I." This indicates that the subject is speaking in the first person, and the action is happening in the present or near future.

2. Future Tense:
The phrase "by 6 o'clock" indicates a specific time in the future when the action is expected to be completed.

3. Future Perfect Tense:
The verb "shall have finished" is in the future perfect tense. This tense is used to express an action that will be completed before a specific time in the future. It consists of the modal verb "shall" (used with the first person) or "will" (used with second and third persons) followed by "have" and the past participle form of the main verb.

4. Past Participle:
In this case, the past participle of the verb "to finish" is "finished."

Putting it all together:
Considering all the above points, the correct answer "shall have finished" indicates that the subject will complete the action of finishing something before 6 o'clock in the future.

Example:
"I shall have finished this report by 6 o'clock." This sentence implies that the speaker will complete the report before 6 o'clock.

Overall, the use of the future perfect tense in this sentence conveys a sense of completion of the action before a specific time in the future.