She took the news calmly.

Literal

She [topic-は] news [object-を] calmly received-it.

受け止める is more vivid than just 受ける — literally 'receive-stop,' meaning to take something in fully and process it (news, criticism, a thrown ball). It implies active acceptance rather than passive receipt. 冷静に is the adverbial form of the na-adjective 冷静 ('cool-headed, calm'), built by the adjective + に. 知らせ is the noun form of 知らせる ('to inform'), so literally 'a thing-of-informing.'