Read Acts 21:26 Using Other Translations
Then Paul took the men, and the next day purifying himself with them entered into the temple, to signify the accomplishment of the days of purification, until that an offering should be offered for every one of them.
Then Paul took the men, and the next day he purified himself along with them and went into the temple, giving notice when the days of purification would be fulfilled and the offering presented for each one of them.
So Paul went to the Temple the next day with the other men. They had already started the purification ritual, so he publicly announced the date when their vows would end and sacrifices would be offered for each of them.