Here are the sentences with "either" or "neither" and the correct helping or modal verbs:

1. My neighbors don't like the noise from the traffic, and I **neither** **do**.
2. He isn't interested in moving to another state, and **neither is** she.
3. Ali can't swim, and **neither can** his friend, Richard.
4. I don't want these old clothes, and they **neither do** he.
5. She hasn't seen that movie, and **neither has** he.
6. You shouldn't overeat, and your kids **shouldn't** **either**.
7. Denise didn't come to class yesterday, and George **didn't** **either**.
8. My dog won't go into the water, and **neither will** my cat.
9. You're not hungry, and **neither am** I.
10. He hasn't had any problems with his Toyota, and his sister **hasn't** **either**.

Feel free to ask if you have any more questions!