The discussion of Acts 15 is a public meeting and Paul's confrontation of Peter in Galatians 2 is personal in nature. Moreover, nowhere is a public decision or letter sent by attendees of the Jerusalem Council mentioned in Galatians. We read in Paul's epistle that he made two visits to Jerusalem. James advocates for Gentiles in Acts 15 and it is Paul who plays a similar role in Galatians 2. How are we to settle this matter?
One theory advanced to resolve this difficulty is that Paul in Galatians 2 was not so much referring to Acts 15 but to the incident of famine relief in Acts 11:27-30. Paul having been prompted by a revelation to make a second journey is consistent a prophecy uttered by Agabus (Galatians 2:2). He also speaks of keeping the needy in mind (Galatians 2:10). The Apostle Peter's hypocrisy relating to eating with Gentiles fits the context of Acts 10-11.
Duke University New Testament scholar Mark Goodacre takes a different approach to this question, noting the style of Greco-Roman biographies. His point of view has been outlined as follows:
"Goodacre describes Acts 9 as a type of “flash forward” of the events described in Acts 11. But it might be better to think of Acts 11 as a “flashback” to the events of Acts 9, which might fit in well with the use of such compositional devices found in other Greco-Roman biographies. It would be reasonable to suggest that Luke effectively repeats the story of Paul’s first visit to Jerusalem, between Acts 9 and Acts 11, to tie those passages together. In the interim, Luke in Acts 9:32 to Acts 11:18 picks up the story of Peter, specifically focusing on the story of Cornelius, the Gentile Roman military officer, and his conversion to Christ. Once done with the story of Peter and Cornelius, Luke recalls where he earlier stopped off with telling Paul’s story, and to bring things back to Paul’s first visit to Jerusalem. Why does Luke do this? We can not be completely certain. It is quite possible that Luke’s objective in Acts is to narrate how the church grew from being a Jewish-only movement to becoming a Jewish-Gentile movement, centered around the mission of Paul, a converted Jew to Christ, to share the Gospel with the Gentiles. In other words, Luke selects material from the history of the early church, to focus first on Peter, and then to transition to the character of the apostle Paul. It would only be fitting for Luke to build up the story of how the church overcame the problems between Jew and Gentile, by temporarily highlighting the background and story of Peter’s interactions with Cornelius, before returning to his main narrative, following the apostle Paul."