What can my neighbor complaining about noise do to me?

what you can do is get with the next door neighbors and see if they are willing to sign a statement about you are not causing too much of noise during that time frame. Also if you can afford it i would get a video recorder and hook it up at these times and record what you are doing as far as watching the tv, if the above person should come down to knock on your door than you would have proof that the tv volume is not that loud and show it to the manager.