Q: I use my thumb print to turn on my iPhone 6.  Now it says it doesn't recognize my thumb.  Is there any other way to turn it on?

You can enter the Passcode that you have had to create when you set up Touch ID.

BTW, you can add multiple fingers to Touch ID, not just your thumb.

Your thumb print is not used to turn on the iPhone. It is only used to unlock it once it's been turned on by either pressing the home button, or pressing the power/sleep button.

If your fingerprint is not being recognized, you can enter the passcode you set up when setting up your fingerprints.

Once unlocked, you can go into Settings->Touch ID & Passcode, and delete and re add your fingerprint. 

Is it asking you for your Passcode (4 or 6 digit number) or for your Apple ID password?

Whats the exact text of the message that you're receiving?

You can also just Try a simple Reset: hold down the Home and Power buttons until you see the Apple logo (10-20 seconds).

The iPhone has been disabled due to too many incorrect passcode or Touch ID attempts.

You'll need to connect it to a computer running iTunes, and restore the iPhone.

If you forgot the passcode for your iPhone, iPad, or iPod touch, or your device is disabled - Apple Support