- What did you do at this time yesterday?
- What were you doing at this time yesterday?
The simple past tense or the past continuous tense?
I wish teachers would stop pretending that there is a straightforward answer to questions like this.
As is usually the case for questions of aspect in English (continuous or not; perfect or not) both options are equally good, and depend not on the external circumstances, but on what the speaker is choosing to focus on.
Option 1 treats whatever you did as a completed act; option 2 chooses to treat is as a continuous activity that it is possible to be in the middle of.
(Note that neither of these options suggests any conclusion whatever about whether the action took a short or a long time - they are about temporal focus, not objective reality).
In the absence of any other cues, "at this time yesterday" suggests a point in time, and therefore (as Kate Bunting suggests) the continuous is probably more natural, as it has the idea of an activity that was in progress at this time yesterday. But other contextual cues could equally well point in the other direction. If the other party has listed a number of actions they took at particular times, then option 2 would make sense.