町 doesn't mean "house", so the question is a little confusing.
It means something like "town" or "neighborhood".
As for a mnemonic to help you with that, I think we would need more information. What kind of mnemonic are you imagining? And do you just care about the word まち or do you want a mnemonic for the kanji too?
I'm not aware of it meaning "house", think it essentially means "street", but since Japanese takes a relaxed attitude to distinguishing singular and plural, it can also mean "town", because a town is just a bunch of streets. To remember that, I just imagine that the "rice paddy" radical on the left looks like a grid of streets on a map. The right radical is trickier though. Maybe imagine it's an umbrella, and picture scene of people walking the rainy streets with umbrellas? It's sometimes known as the "nail" radical, if you can remember that, I guess a town is built with a lot of nails. Yeah, that one's weak.
Using wanikani's mnemonic for the meaning: https://www.wanikani.com/kanji/%E7%94%BA
And for the reading: https://www.wanikani.com/vocabulary/%E7%94%BA
This does kinda rely on you knowing the nail-looking part is the 'street' radical, but except for that this is pretty memorable for me. If in doubt for mnemonics, always give https://wanikani.com a try :)
Mnemonic
What is a good mnemonic to remember Machi is House?