Neither you nor your sister should . . . . . . . . to them.

Answer: Option A

The appropriate verb form to be applied in the given sentence is talk.
As the sentence is in simple future tense the participle used is a simple form.
The options C and D cannot be applied as the tense of the verb is different from that of the sentence given. Talked is in past tense and Talking is in continuous tense.
Option B is inappropriate as there are two subjects in the sentence and so the verb is plural, talk.