The best revision of the wordy sentence is A) The brown dog sitting under the table belongs to the next-door neighbor.
Option A) is the correct one because<u> the phrase "that is brown"</u>, which is postmodifying the noun, <u>has been eliminated and "brown" has become a premodifier of "dog" instead</u>. Therefore,<u> this change makes possible to express the same idea using less words</u>. Moreover, the conjunction "and" and the defining relative clause "who happens to live next door" have also been deleted.<u> The adjective "next-door"</u>, which is modifying "neighbour",<u> is replacing the defining relative clause and, at the same time, making the sentence less wordy</u>.