From the information given, we can calculate that 7/10 of Andy's collection is either action or comedy. This means that Andy is incorrect, because he said that only 4/9 of his collection is action or comedy.
To see why Andy's estimate is too low, consider that 3/5 of the DVDs are action, which is greater than 4/9. Additionally, 1/4 of the DVDs are comedy, which is also greater than 4/9. Since some DVDs are both action and comedy, the total fraction of the collection that is either action or comedy is greater than 4/9.
Therefore, Cynthia is correct that Andy made an error in his estimate.