Paul had grounds to boast because Gentiles had come to Jesus Christ through his ministry. Notwithstanding he gave all the credit for what had happened to Jesus Christ. He had worked through His servant to bring the Gentiles to obey God in word and deed. Obedience in this context involved coming to Christ (cf. Romans 1:5; Romans 16:26; Acts 17:30; 1 Peter 1:2)[source]