When Paul commends Phoebe to the Romans in the first two verses, he is doing for her what his co-worker and friend, Barnabas, did for him years ago.
After Paul/Saul met Jesus on the road to Damascus, he decided to follow Jesus. He immediately began preaching in Damascus that Jesus was the Son of God. Later when Paul went to Jerusalem, the Jewish Christians around Jerusalem found it difficult to trust this guy who had been hunting them down and persecuting them.
At that point, Barnabas stepped forward and commended Paul to them (Acts 9:27: “But Barnabas took him and brought him to the apostles. He told them how Saul on his journey had seen the Lord and that the Lord had spoken to him, and how in Damascus he had preached fearlessly in the name of Jesus.”) Because of Barnabas’ commendation, Paul was trusted and let into the life of the church in Jerusalem.
In Romans 16, Paul is passing on that favor for Phoebe who is believed to be the person taking Paul’s letter to Rome and reading it to the believers there. She is a leader in the church in Cenchreae and has been a benefactor to Paul. He knows her, trusts her and commends her to the Romans.
