。
My sister asked me to teach her to ski.
Literal
Younger-sister [subject-が] skiing [object-を] teach want [quotative-と] me [target-に] asked-came.
~てほしいと頼む ('ask someone to do X') embeds the desire ~てほしい inside a quotative と before 頼む ('to ask/request'). 頼んできた uses ~てくる to convey the request came toward the speaker.