Monitor out is for video out, to the tv (usually), when you send all the video sources through the receiver, for easy video switching, from one source to another.
I've never seen a "multi out" on a receiver, so I don't know about that. I've seen "multi in" (5.1 inputs) though. That's for dvd players with sacd and dvd-a capabilities. You use six analog cables out from the dvd player, into the 5.1 inputs, on the receiver, and use the "Multi Channel" mode, instead of dvd mode, for listening to the High Resolution 5.1 surround music discs. You also use the digital output from player to receiver, for watching movies and listening to redbook cds.
I'm not familiar with HK receivers, so if there's a "multi out" on it, I don't know what it's for. The owner's manual should explain it. I also don't have multi zones, so not very familiar with their settings either.
Good luck!
