Minecraft Local Area Network

Is it possible to play Minecraft with a local area network? I've been trying a hamachi server but when I try to login with the hamachi IP and 25565 as my port. I receive an error: Internal exception: java.io.IOException: Bad packet id 14 and the server log tells me it was a bad login. Do I need a premium account to do this?

Make sure in your server properties file your online-mode is set to false like this video;