Questions & Answers about tā de shǒu shàng yǒu xuè.
的 is the common particle used to show possession or description.
So:
- 他 = he / him
- 他的 = his
- 他的手 = his hand / his hands
In this sentence, 他的手上 means on his hand or on his hands.
上 literally means on, above, or on the surface of.
So:
- 手上 = on the hand / on one’s hand(s)
Chinese often uses a noun + location word like this:
- 桌子上 = on the table
- 墙上 = on the wall
- 手上 = on the hand
So 他的手上有血 is literally something like On his hand, there is blood.