Freddy has a shelf that is 72/5 inches wide. How many catalogs can Freddy arrange on the shelf if each catalog is 4/5 of an inch thick?

The number of catalogs that Freddy can arrange on the shelf is given by dividing the width of the shelf by the thickness of each catalog: (72/5)/(4/5) = 72/4 = <<72/4=18>>18 catalogs. Answer: \boxed{18}.