NKJV - 6 Now when they had gone through Phrygia and the region of Galatia, they were forbidden by the Holy Spirit to preach the word in Asia.
For follow-up discussion and general commentary on the topic. Comments are sorted chronologically.
It looks to me that John the evangelist was entrusted with Asia. As we see in Revelation 1:4 John writes to the seven churches in Asia which he had established.
Look at 1 Peter 1 - "Peter, an apostle of Jesus Christ,
To those who reside as aliens, scattered throughout Pontus, Galatia, Cappadocia, Asia, and Bithynia,"
And look at Romans 15: 20 -
"And thus I aspired to preach the gospel, not where Christ was already named, so that I would not build on another man’s foundation;"
It is possible that Paul did not want to go where Peter had planted churches so there would be no one saying they were with him or with Peter as 1 Corinthians 1:12 and 3:4