。
She explained how to make the cake.
Literal
She [topic-は] me [to-に] cake's making-method [object-を] explained [for me-てくれた].
The productive ~方 nominalizer — verb i-stem + 方 (かた) = 'way of doing X.' 作り方 ('how to make') is one of the most everyday uses, on cooking shows, in recipe books, and on YouTube tutorials. The same pattern gives 食べ方 (how to eat), 使い方 (how to use), 言い方 (how to say). The ~てくれる auxiliary keeps the gratitude framing — she didn't just explain, she explained for me.