Q: iPhone 6 (ATT) will not receive texts, but sends texts with no problem.

Hello 1wrc,

That is interesting that you are able to send but not receive them. Let's see if we can figure out what is going on. 

The one thing that comes to mind is that it could be a blocked number. Check your blocked list by going to Settings > Messages > Blocked and uncheck any numbers that you don't want blocked.

Another thing to check for is a carrier update. This would be for SMS and MMS messages that show up green and not processed through iMessage.

Take a look at the article below for more details troubleshooting issues with sending as well as receiving them. 

If you can‘t send or receive messages on your iPhone, iPad, or iPod touch
https://support.apple.com/en-us/HT204065

Take care