I have to disagree with Carlos. I am a native spanish and we rarely say that (Me gusta el carro de ellos). It is grammatically correct though, but sounds a bit weird and not natural. We say "Me gusta su coche" Notice that if you say "sus" instead of "su" you're expressing that you like their cars (plural) Even when the subject is plural (ellos) the possesive is "su", as long as the posessed thing is not plural.

La respuesta correcta sería: Me gusta el carro de ellos.

The verb only goes plural if you like two things (if your neighbors have two cars). If they are a couple but only have one car, you'd say "Me gusta su carro", the same as if your neighbor was just one. So the only way to make it clear is from context. Either that, or you can say the whole sentence without the possesive pronoun: "Me gusta el carro de mis vecinos"