。
She strongly urged him to take that job.
Literal
She [topic-は] he [to-に] that work [object-を] do [such that-よう] strongly urged.
~ように (clipped to ~よう before another verb) introduces an indirect directive — 'such that (someone does ~).' 勧める ('recommend, urge') naturally takes this pattern, with the recipient of the urging marked by に. 強く is the adverbial form of the i-adjective 強い.