Problem solved.
I have a 2014 Audi Q5. A new iPhone 6 would sync to the car, but either of two problems would occur. Either 1) I could use Bluetooth for calls but would not have any audio whatsoever while iPhone 6 was synced, or 2) the car would "phantom" dial a random number from my iPhone contacts and when I dialed a number, it would then ring once then drop from the car--meanwhile the call would continue on the iPhone.
After deleting and re-syncing over and over, resetting network settings, hard reboot of the iPhone, nothing worked. So, I got on Apple Chat today with a support rep who suggested it might be a corrupt operating system on the iPhone 6. So, he had me backup my iPhone to iTunes. Then, within iTunes, we did a "Restore iPhone." It took about 30 minutes. Then, he instructed that when the iPhone 6 restarted, do nothing to restore the backup or set up any network or wireless, etc. First thing was to try Bluetooth syncing with the car. And lo and behold, it worked. It seems like everything is working fine. Thank goodness.
Now, I just have to slowly restore my backup into my iPhone. I'm hoping to be able to do it piecemeal. If not, I might just have to re-set up the iPhone 6 by hand.