。
She acknowledged that my offer was a fair one.
Literal
She [topic-は] my offer [subject-が] proper one [is-である] thing [object-を] acknowledged.
A multilayered nominalization. The clause 私の申し出が正当なものである ('my offer is a fair one') uses the formal copula である and the noun もの ('thing, one') to describe the offer's nature. The whole clause is then nominalized with こと and marked with を as the object of 認める ('to acknowledge, recognize, accept'). The pattern [clause]+ことを認める is the standard Japanese way to express 'acknowledge that X' — a productive frame across legal, business, and reflective contexts.