The instruction had been posted several times already, basically what you need to do:
1. Download Brown Dust 2 from google play
2. Login with google account
3. Immediately quit the game after login
4. Open file explorer app and search for
com.neowizgames.game.browndust2 (located in OBB folder)
5. Rename it to any or move it to somewhere else (to prevent the folder being deleted- step 6)
6. Now delete/remove the Brown Dust 2
7. Install Brow Dust 2 mod
(signed one) but do not run it yet !
8. Go back to file explorer app, move/rename back the folder to
com.neowizgames.game.browndust2 into OBB folder
9. DONE ! Run the mod and you should able to login google account
If you still don't understand, you need to upgrade your brain cells...