She was worried about his health.

Literal

She [topic-は] his [genitive-の] health [genitive-の] thing [subject-が] worry was.

Two ways of expressing worry coexist in this sentence. 心配だ (with 心配 as a na-adjective + だ) takes its worried-about thing with が, treating 心配 as a state. Compare with 心配する (verb) + を, treating worry as an action. Adding ~のこと ('the matter of') softens or generalizes the topic — 健康のこと is broader than just 健康, including 'how he's doing health-wise.' A common conversational hedge.