According to Galatians 2:8, what were the separate fields for Peter and Paul?

Galatians 2:8 shows that the power working in Peter was for the apostleship to the Jews, while the same power worked mightily in Paul toward the Gentiles. Peter’s field was the circumcision; Paul’s field was the uncircumcision, as the surrounding verses explain.

Les explains that when the Jewish leaders in Jerusalem—Peter, James, and John—perceived the grace given to Paul, they recognized that the same power that wrought effectually in Peter for the apostleship of the Jews was mighty in Paul toward the Gentiles. They gave Paul and Barnabas the right hands of fellowship, agreeing that Paul and Barnabas should go to the heathen/Gentiles while they would go through circumcision. This was decided in 51 A.D., 13 years after Peter had gone to Cornelius. Paul stood his ground against Jewish believers who insisted Gentiles must become proselytes of Judaism, and because he did not give in, we have this tremendous gospel of grace.

Galatians 2:8

(For he that wrought effectually in Peter to the apostleship of the circumcision, the same was mighty in me toward the Gentiles:)

What does Galatians 2:8 teach about God working in Peter and Paul?

Galatians 2:8 teaches that the same God who worked effectually in Peter for the apostleship of the circumcision, meaning Israel, also worked mightily in Paul toward the Gentiles. It shows one God empowering two distinct apostolic ministries: Peter to Jews and Paul to Gentiles.