en_tn/act/21/26.md

took the men

These are the 4 men who made a vow.

he purified himself along with them

Before entering the temple area the Jews were required to be ceremonially or ritually clean. This cleansing had to do with Jews having contact with Gentiles.

went into the temple

They did not go into the temple itself where only the high priest was allowed to enter. They entered the temple courtyard. Alternate translation: "went into the temple courtyard" (See: rc://en/ta/man/translate/figs-synecdoche)

the days of purification

This is a separate purification process from the purification process which they were required to fulfill in order to enter the temple area.

the offering would be presented

This can be stated in active form. Alternate translation: "they presented the animals for an offering" (See: rc://en/ta/man/translate/figs-activepassive)