1. In three minutes, he started to shout.

2. After three minutes, he started to shout.

(Which preposition should we use? Which one is right?)

3. Three minutes later, he started to shout.

4. Some minutes later, he started to shout.

5. After a short time, he started to shout.

6. After a moment/second/minute, he started to shout.

(Are they all grammatical? thank you.)

They are all correct. However, 1 is not clear.

1. In three minutes, he started to shout.

2. After three minutes, he started to shout.

Both sentences are grammatically correct, but they convey slightly different meanings.

1. "In three minutes, he started to shout" implies that after the passing of three minutes, he started shouting. It indicates a specific duration of time, as if you were counting down the minutes until he started shouting.

2. "After three minutes, he started to shout" suggests that he started shouting once three minutes had elapsed. It emphasizes the point at which three minutes had passed.

3. Three minutes later, he started to shout.

This sentence is also grammatically correct. It is a concise way of expressing that he began shouting three minutes after a certain event or reference point.

4. Some minutes later, he started to shout.

This sentence is grammatically correct, but it is less specific than the previous examples. "Some minutes later" is a more vague term, suggesting that an indeterminate amount of time passed before he started shouting.

5. After a short time, he started to shout.

This sentence is grammatically correct and conveys the idea that he started shouting after a brief duration. The term "short time" is subjective and could vary depending on context.

6. After a moment/second/minute, he started to shout.

These sentences are all grammatically correct and convey a similar idea that he began shouting after a very brief moment or duration of time. The specific choice of moment, second, or minute implies different lengths of time, with "moment" being the shortest and "minute" being the longest in this context.