There are many inferences to be had, but they relate mostly to the numerical distributions. We know that the gerbils and hamsters will be in cages W and X. We also know that the snakes and lizards will be in cages Y and Z. Since each cage has exactly 2, 4, or 6 pets, we can limit the numerical distributions pretty quickly.
The gerbils and hamsters will have 4 pets in one cage and 2 pets in another. Since we cannot place only hamsters or only gerbils into a cage, we'll end up with 2 gerbils and 2 hamsters in one cage and 1 gerbil and 1 hamster in the other.
The snakes and lizards are slightly more flexible, but we'll have one cage with at least 2 snakes and 2 lizards, another cage with at least 1 snake and 1 lizard, with two more snakes to place in either cage.