。
She agreed to take the criticism.
Literal
She [topic-は] that criticism [object-を] receive [nominalizer-こと] [to-に] agreed.
~に同意する ('to agree to / consent to') takes its target with に — the thing being agreed to. Here the target is a nominalized clause: 受けること ('the receiving'), with こと turning the verb 受ける into a noun-like unit. 非難を受ける is a set collocation for 'receive criticism, take blame' — 非難 implies serious censure, more weight than ordinary criticism. The whole sentence has a touch of formality, the kind of phrasing that might appear in a news report on a public figure's response to scrutiny.