The correct answer is: by.
The preposition “by” is used to indicate a specific time or point in time. In this case, the speaker is saying that they will have finished their homework by the time the other people arrive. This means that they will be done with their homework before the other people arrive.
The other prepositions in the options have different meanings. “Until” and “till” are both used to indicate a period of time up to a certain point. In this case, they would mean that the speaker will be working on their homework until the other people arrive.
“By the time” is the most specific of the options. It indicates a specific time or point in time, while “until” and “till” can be used to indicate a period of time up to a certain point.
Here are some examples of how the preposition “by” can be used:
- I will be home by 6pm.
- The meeting will start by 9am.
- The store closes by 10pm.
- I will have finished my homework by the time you arrive.