Hand-to-hand fighting is fighting at very close range, where people use their hands, and often knives or other small weapons, rather than guns from far away. News and army English say hand-to-hand combat. You use it before a noun: hand-to-hand fighting. Though actually, it does not mean people only use bare hands — knives count; the point is you are close enough to touch the other person. It has nothing to do with shaking hands, and nothing to do with handing something over.