。
I hear she turned down his proposal.
Literal
She [topic-は] his [genitive-の] proposal [object-を] declined [hearsay-そうだ].
~そうだ here is the hearsay reading — 'I hear that, it is said that' — distinct from the appearance reading also written ~そうだ. They differ in attachment: hearsay attaches to plain forms (断ったそうだ, 'I hear she declined'), appearance attaches to verb stems and adjective stems (断りそうだ, 'looks like she'll decline'). Same surface, different morphology and meaning.