How do i mute parts of a video?

There are very, very few situation when you should edit or process audio in After Effects.  YOu should almost certainly be working in Premiere or Audition.

Hi. Toggle open the layer then toggle open Audio. Set a keyframe at the beginning and at the end of the silence, then go passed the first keyframe and turn the audio down (it will create a keyframe), then go to just before the next keyframe and turn the audio down there as well. You can set the fade up/down by moving the two interior keyframes.