manipulate, rule, administer, conduct, palm of hand

彼の手のひらに硬貨を置く。

Place a coin in the palm of his hand.

彼は手のひらで一撃を与えた。

He gave a blow with the flat of his hand.

今度は話題が途切れないように手のひらにリストアップしとこう。

This time, so I don't run out of things to talk about, I'll write a list on the palm of my hand.