My iPhone 6 Plus does not ring when called.

You've probably done this already, but have you checked that the side button is not switched to 'red' to mute calls, or that 'Do not disturb' hasn't been accidentally enabled?

If either of those aren't the cause, have you tried a hard reset - restart holding the on/off button and home button until you see the phone reboot with the Apple logo on screen.

Is i possible that you have "Mute" option turned on? Check the button on the left side. If you see red line - mute option enabled(see picture )

You're welcome. I've done exactly the same, that's why I thought it worth a mention 😀.