I switched to AT&T but my Iphone6 purchased abroad doesn't accept the new carrier. What should I do?

Hello Koukino, the same problem happened to me when I came to the US and an IPhone bought in India but luckily I found a friend majoring in electronics who helped figure this out. Hope this will help you as well;

Remove your SIM card and insert the new SIM card.
Complete the setup process.
Restore your iPhone to factory settings.
Try the automatic detection of carrier and if it doesn't work do it manually and choose AT&T
Reboot it (click at the same time on home and lock/unlock button for 30s then the home button for 10s)
Leave it 12hours in airplane mode
Activate it. It will ask you to reconfigure it again.
And then it will work.

So this is it. If it doesn't't work with you this way try it another time. If not;
Contact your carrier to make sure that they can unlock your iPhone with your carrier's system.
Restore your iPhone from a backup.