I see that the display of your iPhone 6 Plus has stopped responding. Good job with trying a restore to fix this issue, and I'm happy to help.
Get help with the display on your iPhone, iPad, or iPod touch -- The step to correct a non-responsive display is to force-restart the device. Since you've already attempted restoring and the issue persists, it's time to have your phone evaluated.
Contact - Official Apple Support -- Apple Support can troubleshoot this issue further with you and supply you with your service options if necessary. You can get support by phone or chat, set up a repair, or make a Genius Bar reservation for iPhone, iPad, iPod, Mac, and more.
Find Locations -- You can also locate the nearest Apple Store or Apple Authorized Service Provider if you'd rather. Make sure the country you're located in is showing on the top-right corner. If it isn't, click it and choose the correct one.
Get your iPhone, iPad, or iPod touch ready for service -- In case service is called for, before you take or send your iPhone 6 Plus in, make sure it's ready for service.