Select the most appropriate option to fill in the blank.

She ________ her painting by this time next week.

The correct option to fill in the blank is will have finished.

Detailed Explanation:
The sentence structure indicates a timeline with a specific deadline in the future: "by this time next week".
When a sentence describes an action that is expected to be completed before a certain point or deadline in the future (often introduced by the preposition "by"), we use the Future Perfect Tense.

The Future Perfect Tense is constructed as follows:
Subject + will have + past participle (third form of the verb)

Applying this template to the verb "finish":
- Subject: She
- Future Perfect Auxiliary: will have
- Past Participle: finished

This gives us the complete, grammatically correct sentence:
"She will have finished her painting by this time next week."

Why other options are incorrect:
- will finish (Simple Future Tense): This expresses an action that will happen in the future, but it does not specify or emphasize completion relative to a deadline like "by this time".
- finishes (Simple Present Tense): This is used for habits, general truths, or fixed timetables, which is incorrect here.
- finished (Simple Past Tense): This refers to an action completed in the past, which directly contradicts the future reference "next week".