The correct option is
D for
The sentence indicates that the subject hasn't had a peaceful during the last six months. Thus, the answer must mean 'during'.
Option A is incorrect. 'from' is used to indicate or specify a starting point, it does not mean 'during'. Thus, it does not have the required meaning and is not the correct answer.
Option B is incorrect. 'at' means 'in, on or near' and not 'during'. Thus, it does not have the required meaning and is not the correct answer.
Option C is correct. 'for', in this case means, 'during'. It has the correct meaning and so, it is the correct answer.
Option D is incorrect. 'since' means 'from then till now' and not 'during'. Thus, it does not have the required meaning and is not the correct answer.