。
She tried to talk him out of joining the project.
Literal
She [topic-は] him [to-に] that project [in-に] not-participate [so-as-to-ように] tried-to-persuade.
A neat layering of grammar. ~ように attached to a negative verb gives 'so as not to do X' — 参加しないように means 'so as not to participate.' This phrase serves as the content of the persuasion: she's trying to persuade him *not* to join. 説得する ('persuade, convince') takes に for the person being persuaded and ~ように for the goal-content. The closing ~ようとする marks the action as an attempt — 'tried to' — and crucially doesn't say whether she succeeded; the attempt and the outcome are separate facts in Japanese.