After my great experience with Ubuntu Mate, I convinced my brother to install it as well. He likes it so far, but the System not re-staring or shutting down. When he is trying to restart it, a black screen lingers on indefinitely. When he is trying to shut it down, the default green screen lingers on indefinitely. I launch this problem today, please send your solutions, but I will not be able to review it until tomorrow. Thank you for your patience!
Press ctrl-alt F1 (or F2 or F3 etc) to switch to a tty.
Login using your usual username and password.
Then type the shutdown command. (Enter your password when prompted).
sudo shutdown
The system messages will be printed to the screen. There might be a timeout while a process is terminating. If not, what message does it seem to hang on?
If the last message is something like "shutting down" (I can't remember exactly) then walk away and see if it has completed shutdown 15 minutes or so later.