I have two houses.
One is horde, lvl 12.
Another one is Alliance, lvl 6.
I want to leave the current guild the lvl 12 horde house is in, and I would like to relocate to my ALLIANCE guild with my lvl 12 house.
What would be the best way to do it? I can relinquish the lvl 6 house if needed.
Nope. Horde house can only go to another Horde neighborhood.
Yeah, the houses are tied to the faction of the neighborhood. You can move houses without losing the XP but a house started in a horde neighborhood can only be moved to another horde neighborhood.
I would suggest making sure all of your characters have the alliance neighborhood endeavor active so you can earn XP on that house faster. From your house level numbers, it sounds like you have always left your horde neighborhood endeavor active. You can pick up a lot of housing XP from just doing world quests and raids (old or new). If your Alliance neighborhood has one of the newer endeavors, you can also do a lot of easy tasks in the neighborhood to build up your house XP as well.