Hi there larry.mcgill,
Thanks for stopping by the Apple Support Communities! It sounds like the Snapchat app on your iPhone 6 is grayed out, despite trying to restart, back up, sync your device, and delete the app. I'll be more than happy to provide some suggestions to resolve this.
To begin, go to Settings>General>Storage & iCloud Usage. From there, tap on "Manage Storage" under "Storage". You should see a list of your apps populate after a moment. Scroll through and locate the Snapchat app. Tap on it and see if it will allow you to delete it from there. If so, you can go back into the App Store and reinstall it.
If you're unable to remove the app that way, you can try to reset the settings on your iPhone. To do that, go to Settings>General>Reset>Reset All Settings. This won't remove any of your personal data. You may need to adjust some of your user-specific settings (e.g. wallpaper, etc.), as well as re-enter your Wi-Fi login information.
Beyond that, you'd want to look at resetting your device to factory settings to rule out any software issues. This would install a fresh copy of iOS on your iPhone. Once you test out that you're able to access Snapchat, you can restore from a backup. Here is a link with information on how to restore to factory settings:
Use iTunes on your Mac or PC to restore your iPhone, iPad, or iPod to factory settings
Have a wonderful rest of your day!