Noun and の adjective
ひだりきき
なぜかいつも左利きの女せいにひかれるんです。
For some reason I'm always attracted to left-handed women.
左利きの人向けの仕事に力を入れています。
I'm buckling down on work for left-handed people.
「どういったご用件でしょうか？」「あなたが左利きかどうかだけ知りたいんですが。」「あいにくそれはお伝えできないことになっております。」
"May I ask the purpose of your call?" "I just want to know if you are left handed." "I’m afraid I’m not at liberty to disclose that information."
If you profit from the left, you're probably doing everything on the left. That's your good side. You're probably left handed.
The readings are the kun'yomi vocab readings, so combine the readings of the words 左 and 利く together to get the reading of this one. It makes sense since this word is like two words put together.