Question

a small quantities of water and Acetone are placed on the palm of both the hands which will experience more cooling

Answer 1

the palm on which the acetone is kept will feel more cooling because the rate of evaporation of the acetone is high than of the water

Answer 2

Acetone is a volatile solvent (it evaporates easily) so it absorbs much heat when evaporating, and your skin gets colder because of that. So acetone is not "colder", it just cools down your skin more easily when evaporating.

here is your answer.☺️