Motorola Moto G2: Unable to pick incoming calls most of the time I'm unable to pick incoming calls, nearly 8 out of 10 times on my device. The calling party thinks that I am trying to avoid them.
Try booting into "SAFE MODE" and see if the problem persists (long press the power off option and select 'OK' in the pop up to boot into safe mode). If you are able to Accept/Reject calls (while in Safe Mode) then the problem might be due to a third  party application installed on your phone, probably a screen filter app/ third party launcher. Reboot the phone to boot into normal mode and try uninstalling any application you suspect and see if your problem is solved.

If the above method doesn't work then it might be a bug which will probably be rectified by Google soon in the next update.

Else as a last resort you can "Factory Reset" your phone and hope that the problem is solved.