。
She really knows how to handle children.
Literal
She [topic-は] child [genitive-の] handling-method [object-を] well knows-thoroughly.
心得る ('to understand, be well-versed in, have a grasp of') is a slightly formal and decisive verb — stronger than 知る ('know') or 分かる ('understand'), implying not just knowledge but mastery you can rely on. The compound noun 扱い方 ('way of handling') is built from the verb 扱う plus the suffix 方 ('manner, way of'), which can attach to almost any verb stem to form 'how to do X': 食べ方 ('how to eat'), 読み方 ('how to read'). よく adds 'well, thoroughly' — together the sentence praises someone's full mastery of dealing with kids.