Acts 24:11-12 NKJV “because you may ascertain that it is no more than twelve days since I went up to Jerusalem to worship. And they neither found me in the temple disputing with anyone nor inciting the crowd, either in the synagogues or in the city.”
It is sometimes suggested that the only purpose that Paul and the other disciples had for being in the temple was to evangelize Jews. Paul here refutes that idea— his purpose in the temple is Worship. He did not do any preaching there.
Acts 24:14 NIV “But this I confess to you, that according to the Way, which they call a sect, I worship the God of our fathers, believing everything laid down by the Law and written in the Prophets,…”
The word that is translated as “sect” here is used in several places in Acts of various factions within Judaism— Acts 5:17 “sect of the Sadducees”, Acts 15:5 “sect of the Pharisees”, Acts 24:5 “sect of the Nazarenes”, Acts 26:5 “the strictest sect of our religion”. The word does not imply that it is a separate religious community.
Here again, Paul again claims to be faithful to the Scriptures.
Acts 24:17-18 NRSV “Now after some years I came to bring alms to my nation and to offer sacrifices. While I was doing this, they found me in the temple, completing the rite of purification, without any crowd or disturbance.”
Here Paul explains himself clearly. He is participating in temple rites just like every other Jew. He is not preaching; his purpose for being there is private worship.