Nautilus, unless we aren't counting tentacles as legs
Edit: just saw the leg counter has to be at 4, disregard
If tentacles don't count as legs, then nautilus could be the close top corner.
Edit again: fuck, never mind, nautilusses are slimy. The close top corner could be barnacle.
Alright, this may be controversial, but I'm presenting Scarrus Vetula, the Queen Parrotfish as our transcendent chart-topper.
Parrotfish skin is covered in a slimy mucous they secrete that helps repair damage, repel parasites and protect form UV radiation. Slime is a strong YES.
At night, Queen Parrotfish vomit up a big glob of mucous which they hide in while the sleep. Here's a video. Every Queen Parrotfish has exactly 1 house that they sleep in at night so should also be a yes.
Legs is where things get tricky. If fins cannot count as legs then our discussion ends here. Queen Parrotfish are fish. They don't have walking limbs only swimming limbs, the legs of the see.
But sadly, even if you accept that fins can be legs we have not reached the end of our difficulties, as Queen Parrotfish have a topfin, a bottom fin, a tailfin and two fins on either side of their body.
If we take the chart as meaning having at least 4 legs not exactly 4 legs, or accept only side fins and not top, bottom or tail fins as being legs then we are home and (heh) dry.
If not, then you have no choice but to snub the Queen Parrotfish (he/she/they/them will remember this) and begin your search for the 4 legged Slimy: Yes house 1 creature anew.
New struggle session just dropped:
Swimming limbs; legs of the sea, or arms of the sea?
Arms are just a fancy type of leg. Nearly everything with arms can walk on them, but nearly nothing with feet can pick things up with them.
Just did four hours of algebra. This makes more sense to me than anything I paid to study.
I think you won. According to this link
"Soft-shelled turtles have a naturally occurring layer of bacteria or “slime” like a fish."
It's really tough to describe an absurd innanimate object which is also a creature without making it sound like a final fantasy miniboss. Pretty sure FFVII remake makes you fight a four-legged slimy house.
Crabs have 10 legs, which I guess could count, there's nothing that says going over isn't allowed, but they're not necessarily slimy.
I thought I'd solved it when I realised almost all turtles have algae on their shells making them slimy house 4 legs but then I realised that they were still only a slime probably not a slime yes, and I think crabs only qualify as a slime maybe.