Step 1: What this question tests.
This is a match question about body symmetry in different animal groups. We have to pair each animal with the type of symmetry it shows.
Step 2: Quick idea of symmetry.
Symmetry tells us how an animal's body parts are arranged around a centre or an axis. Some animals can be cut into equal halves in many ways, some in only one way, and some not at all.
Step 3: Match the cnidarian.
Group A is a cnidarian. Many cnidarians show biradial symmetry, which is option II. So A goes with II.
Step 4: Match the echinoderm.
Group B is an adult echinoderm, like a starfish. Adult echinoderms have five-armed or pentaradial symmetry, which is option IV. So B goes with IV.
Step 5: Match the gastropod.
Group C is an adult gastropod, like a snail. Because of its coiled shell and twisted body, the adult gastropod is asymmetrical, which is option I. So C goes with I.
Step 6: Match the fish.
Group D is a fish. Fishes have clear bilateral symmetry, where left and right halves are mirror images, which is option III. So D goes with III.
Step 7: Conclusion.
The complete matching is A-II, B-IV, C-I, D-III. Therefore the correct answer is "A-II, B-IV, C-I, D-III". \[ \boxed{\text{A-II, B-IV, C-I, D-III}} \]