Juan's dog stands 2 feet and 3 inches tall. Peter's dog stands 9 inches tall. How much taller Juan's dog is than Peter's dog.

Juan's dog is 27 inches tall because there are 12 inches in a foot and 15 inches remaining after the 2 feet are accounted for.

Juan's dog is 18 inches taller than Peter's dog because 27 - 9 = <<27-9=18>>18. Answer: \boxed{18}.