**What will you be doing this time tomorrow?**

To understand the correct answer, we need to analyze the question and its context. The question is asking about a future activity happening at the same time tomorrow. Let's break it down:

1. **The Structure of the Question:**
- The question is formed using the future continuous tense, which is used to describe an ongoing action in the future.
- The structure of the question is "will + subject + be + present participle (-ing form) of the verb."

2. **Understanding "will" as the Future Tense:**
- "Will" is the helping verb used to indicate future actions or events.
- In this context, it indicates that the action will take place in the future.

3. **Understanding "be" as the Auxiliary Verb:**
- "Be" is the auxiliary verb used in the future continuous tense.
- It helps to form the continuous aspect of the verb.

4. **Understanding "doing" as the Present Participle:**
- "Doing" is the present participle form of the verb "do."
- In the future continuous tense, the present participle is used to indicate an ongoing action.
- It follows the structure of "be + present participle."

5. **Interpreting the Question:**
- The question is asking about the activity or action the person will be engaged in at the same time tomorrow.
- It suggests that the action will be ongoing or in progress at that time.

Therefore, the correct answer is "will you be doing." This answer follows the structure of the future continuous tense and accurately expresses the ongoing nature of the action at the specified time in the future.