Samsung is yet to provide an Android 4.2.2 update for the Galaxy Note 8.0, but just like last time, it has been leaked via XDA. It is for following carriers, but can be used on any unlocked Note 8.0.
Here is a screenshot of it.
Download the ROM from here and use the ODIN to flash it. Keep in mind that this will erase anything and everything that is stored on your Galaxy Note 8.0, so make sure to make a backup of your tablet before you hit the flash button.
The Android 4.2.2 is more like a bug fix release that adds some important features over the Android 4.1.2 operating system.