The correct option is
C James didn't either
The given sentence suggests that both, Roy and James, did not attend school. Thus, the answer must be in a negative degree. Further, the answer must contain a pronoun that indicates that both, James and Roy did not attend school.
Option A is incorrect. In 'nor didn't James', 'nor' is a conjunction and not a pronoun. Further, the sentence contains two negative words, and having two negatives in one sentence makes it positive. Thus, the answer is incorrect.
Option B is incorrect. In 'neither didn't James', although 'neither' is a pronoun that refers to Roy and James, it contains two negatives. Having a double negative in a sentence will make it positive. Thus it is the incorrect answer.
Option C is correct. 'James didn't either' contains a pronoun 'either' that refers to both, Roy and James. Further the negative 'didn't' suggests that both of them did not attend school. Thus,it is the correct answer.
Option D is incorrect. In 'James didn't too', 'too' is an adverb which is used to indicate an extreme situation. Thus, it does not contain a pronoun that refers to both, James and Roy, and is the incorrect answer