Samsung might have abandoned the Galaxy Note 2 N7100 users on Android 4.4.2 but spirits are still high at XDA whose developers have released Cyanogen Mod 13 for the N7100 that brings Android 6 Marshmallow to the Note 2. Fortunately, everything is working which is a great thing.
Here is what’s working: OpenGL (CPU rendering) , MALI blobs (GPU rendering) , HWComposer and MALI R3P2 drivers , Rotation , Camera , WiFi , Bluetooth , NFC (Android Beam) , Sensors (ALL!) , Vibration , Home Button wake , RIL , GPS , Signal Icon , Soft Keyboard on first boot , Mouse pointer , Pin lock , External media mounting.
Install the ROM (download link) using Note 2 custom recovery like TWRP or CWM and then install gapps. Gapps are not included in the ROM so it is suggested you install it yourself. You can grab the packages from here.