脸上(liǎn shàng) - on the face, on one's face in Mandarin

脸上 is a place word, not a noun in its own right: 脸 plus the locative 上. Chinese needs that suffix before a body part can serve as a location, so where English says "on his face" with a preposition, Chinese tacks 上 on the end instead.

This matters because Chinese existential sentences want a place in subject position. 他脸上有伤 works; 他的脸有伤 sounds off to most speakers. Get into the habit of adding 上 whenever a body part is where something is, sits or lands: 手上, 身上, 头上, 脸上.

Note also that the possessive 的 is usually dropped in this pattern. 她脸上 is far more natural than 她的脸上, and the same goes for family members and body parts generally.