The verb hand means to . . .
hand something down
The phrasal verb hand something down means to give something used to someone else.
I handed my old comic books down to my little cousin.
hand something in
The phrasal verb hand something in means to submit.
I have to hand in my essay by Friday.
hand something out
The phrasal verb hand something out means to to distribute to a group of people.
We will hand out the invitations at the door.
hand something over
The phrasal verb hand something over means to give (usually unwillingly).
The police asked the man to hand over his wallet and his weapons.