。
She did the laundry twice today.
Literal
She [topic-は] today 2 times laundry [object-を] did.
回 is the everyday counter for occurrences or rounds — '2 times,' '3 times,' 'how many times.' Like other counters, it sits between the number and the verb, functioning adverbially without taking a particle. 洗濯をする pairs the noun 洗濯 with the light verb する; the bare verb 洗濯する would mean the same thing, but the [noun]+を+する frame is slightly more deliberate, treating laundry as a discrete activity. The placement of frequency as an adverb (今日２回) is typical Japanese word order: time, frequency, then verb.