The correct answer is: during.
The word “during” means “at the time of” or “throughout the period of”. In this case, the party wants to expel the member because of his anti-party activities during the recent by-elections.
The other options are not as accurate. The word “inside” means “within” or “on the inside of”. This does not make sense in the context of the sentence. The word “through” means “from one end to the other of” or “in a continuous line”. This also does not make sense in the context of the sentence. The word “while” means “at the same time as” or “during the time that”. This is not as accurate as the word “during” because it does not specify that the party wants to expel the member because of his anti-party activities during the recent by-elections.