Hard Reset your iPhone.

When your screen becomes unresponsive, the first thing you should do is hard reset it. This is done on an iPhone 6 by doing the following steps:

1. Press and hold the Home and Power/Sleep buttons at the same time.
2. Wait until you see the Apple logo on the screen.
3. Release the buttons after the Apple logo displays to allow the phone to restart.

iTunes' Factory Reset

If a hard reset doesn't work or the screen remains black, try connecting the phone to your computer and restoring it using iTunes. Here's how to do it:

1. Make sure iTunes is up to date on your PC.
2. Use the lighting cable that came with your iPhone to connect it to your computer.
3. Follow the onscreen instructions if a notification requests your device passcode or that you Trust This Computer.
4. When your iPhone shows in iTunes, choose it.
5. Once iTunes has detected your phone, go to the Summary page and select Restore iPhone... from the drop-down menu.
6. To confirm the action, click Restore.
7. Wait for your iPhone to finish restoring and restarting. Your phone should be in like-new condition. The screen should be operating correctly again by now if the problem was caused by an unknown software bug.