。
She encouraged him to write a novel.
Literal
She [topic-は] him [to-に] novel [object-を] write [in-order-to-ように] encouraged.
励ます ('encourage, cheer up, embolden') used with ~ように marks the desired outcome of the encouragement: 'encouraged him so that he would write.' The ~ように + reporting-verb pattern is consistent across many speech acts: 頼む ('ask'), 言う ('tell'), 忠告する ('advise'), 励ます ('encourage'), 嘆願する ('plead'), 依頼する ('request'), 合図する ('signal'). All take ように for the indirect requested action.