en_tn_lite_do_not_use/act/16/04.md

they went

This pronoun refers to Paul, Silas, and Timothy.

for them to obey

"for the church members to obey" or "for the believers to obey"

that had been written by the apostles and elders in Jerusalem

"that the apostles and elders in Jerusalem had written". (See: rc://en/ta/man/translate/figs-activepassive)

the churches were strengthened

"Paul, Silas, and Timothy strengthened the churches". (See: rc://en/ta/man/translate/figs-activepassive)