Q: Facetime cannot use after update to IOS 6

Is imessage turned on in settings, imessage, on, and how are you trying to use facetime. It is in your contact itself.

Have you activated by signing in for imessage and for facetime. If so you need to restart your phone, if that doesnt work you will need to do a restore in itunes from your backup.

Also look here.

http://support.apple.com/kb/HT4319

Depending on the country you live, and the carrier you have  is whether you have facetime, But it sounds like there is a glitch and you need to do a restore on your phone through itunes, Connect your phone to itunes, click on your name and click on restore from backup.

Your welcome.