。
She likes cooking for her family.
Literal
She [topic-は] family [for-のために] cook [nominalizer-の] [subject-が] like is.
Two patterns work together here. のために ('for the sake of, for the benefit of') marks the beneficiary, and の-nominalization wraps the verb 料理する so it can sit as the subject of 好き. The combination ~のが好きです — 'like V-ing' — is one of the most common ways Japanese expresses an affinity for an activity. Polite ~です makes this a friendly, neutral statement of taste, the kind you'd hear in everyday conversation.