。
She asked Bob to teach her skiing.
Literal
She [topic-は] Bob [to-に] skiing [object-を] teach [for-her-くれる] [in-such-a-way-ように] requested.
This sentence layers indirect speech and the benefactive system. ように頼む is the standard frame for reporting a request ('asked that ~'); it nominalizes the requested action with ように. The benefactive 教えてくれる ('teach for me/us') is embedded inside that — she asked Bob to do the teaching as a favor toward her. From the narrator's perspective, the favor flows toward her, the in-group; using くれる rather than あげる encodes that direction. Without くれる, the request would lose its 'for her benefit' nuance.