Step 1: Understand the matching.
Each feature belongs to one vertebrate class. We match the special organ or structure to the class that owns it.
Step 2: Place Jacobson's organ.
Jacobson's organ is a smell-detecting structure in the roof of the mouth. It is well developed in reptiles, especially snakes. So A goes with Reptilia (IV).
Step 3: Place pneumatic bones.
Pneumatic bones are hollow and filled with air to reduce body weight for flying. These are found in birds. So B goes with Aves (I).
Step 4: Place vocal sacs.
Vocal sacs are air pouches used by male frogs to make loud mating calls. These belong to amphibians. So C goes with Amphibia (II).
Step 5: Place corpora quadrigemina.
Corpora quadrigemina are four rounded bodies in the midbrain. This four-part structure is a special feature of mammals. So D goes with Mammalia (III).
Step 6: Read the final match.
The match is A-IV, B-I, C-II, D-III, which is the first option.
\[ \boxed{\text{A-IV, B-I, C-II, D-III}} \]