Yamashita has a black umbrella in her right hand.
There was a little girl holding a marble in her right hand.
I prefer to use my right foot, right hand, and right eye.
The kanji for "right" and the kanji for "hand." I don't think it gets any clearer than this!
This is a jukugo word, which usually means on'yomi readings from the kanji. This word, however, uses the kun'yomi readings, combined. This is possibly because of 手, which is a body part. When a body part is present in a word, it usually changes to the kun'yomi reading for who knows what reason. Either way, both kanji use the reading you learned in this word, so you should already know it.