The correct answer is Option D.
SHAN'T is the contraction of SHALL NOT.
SHALL is used to express an order or command.
In the given sentence, the speaker is ordering the person to not read a private letter addressed to him/her.
Thus SHALL NOT is the correct answer.
The remaining options are incorrect because:
SHOULDN'T expresses the obligation to not do something.
COULDN'T expresses inabilty.
WON'T is the contraction of WILL NOT.