All you need to do is set up a series of equal proportions. To find the number of cat owners, solve 18/27 = x/18, because you know that the cat owners are coming from the 18 total pet owners, and you know that cat owners and pet owners are in an 18-to-27 ratio as stated in the question. You find that the total number of cat owners = 12.
You also know that the number of houses with more than one cat are coming from the total cat owners, and you know that homes with more than one cat and total homes with cats are in an 18-to-27 ratio as well. So, again, set up a proportion: 18/27 = x/12, and you find that the number of homes with more than one cat = 8.