She asked him to carry her bag.

Literal

She [topic-は] he [to-に] bag [object-を] [carry-want-運んでほしい] [quotative-と] requested.

~てほしい ('want someone to do') combined with 頼む ('ask, request') is a standard way to report a request. The に marks the addressee (the one being asked); the bag is the object of the requested action of carrying.