A transitive verb exerts its action on an object, which means it can only express its meaning completely if that object is mentioned. In the sentence "Rings on the scales of some fish show the age of the fish," the verb is "show". To find the object, we have to ask the verb a question: the rings show what? They show the age of the fish. "the age of the fish" is the complete object of the verb "show". Therefore, the verb "show" is transitive.
