The correct option is C James didn't either
Let’s examine the sentence: “Rose didn't do anything yesterday, and ____ . ” When we see the options, we understand that the blank needs a clause reiterating the fact given in the first clause of the sentence but for James. Hence, the adverb ‘either’ would be used to express the similarity of fact in both the clauses. The adverb ‘either’ means ‘as well’ here. ‘Neither’ cannot be used as the sentence contains the negative, ‘not.’ Neither indicates that the two ideas are linked together. It’s kind of like a negative conjunction. But if you use neither, then make sure your sentence does not have any other negatives preceding it. Now, the tense of the second clause would also be the same as the first clause and to emphasize the fact stated in the first clause, same helping verb as used in the first clause would be taken here. As Option C fulfills these conditions, it is the correct answer. Other options cannot be used as they would make the sentence meaningless.