Until
mother would not let me go out until i finished cleaning my room
easy peasy lemon squeezy

Explanation:
The correct preposition to fill in the blank is option 'c) until'.

Definition of 'until':
'Until' is a preposition that means up to the point in time or the event mentioned. It indicates the time or event that must occur before another action can take place.

Explanation:
In the given sentence, the mother would not let the speaker go out until they finished cleaning their room. This means that the speaker is not allowed to go out unless they have completed the task of cleaning their room.

Example:
To illustrate the use of 'until' in this sentence, let's consider an example:
- The speaker's mother has given them the condition that they can only go out once they finish cleaning their room.
- Until the speaker finishes cleaning their room, the mother will not allow them to go out.

Other Options:
Now let's consider the other options and see why they are incorrect:

a) 'still': The word 'still' is not appropriate in this context because it does not convey the same meaning as 'until'. 'Still' is used to indicate that a situation continues to exist or is ongoing. However, in this sentence, the speaker's mother is imposing a condition that must be fulfilled before they can go out.

b) 'without': The word 'without' is not suitable in this sentence because it does not convey the same meaning as 'until'. 'Without' means lacking or not having something. However, in this sentence, the mother is not allowing the speaker to go out unless they finish cleaning their room.

d) 'upon': The word 'upon' is not appropriate in this context because it does not convey the same meaning as 'until'. 'Upon' means immediately after or as a result of a particular event or action. However, in this sentence, the mother is not allowing the speaker to go out until they finish cleaning their room, not immediately after.

Therefore, the correct preposition to fill in the blank is 'until'.