My older sister has a mole on her left hand.
Please raise your left hand.
I got a light bulb tattoo on my left hand.
The kanji for "left" and the kanji for "hand." Put them together and you have a left hand.
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, oftentimes it gets changed over to 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.