Step 1: The operator site (A) is the binding site for RNA polymerase, which is involved in transcription. Therefore, A corresponds to II.
Step 2: The promoter site (B) is the binding site for RNA polymerase, and it initiates transcription. Hence, B corresponds to I.
Step 3: The regulator gene (C) codes for an enzyme, so C corresponds to IV.
Step 4: The structural gene (D) codes for the repressor protein, and thus D corresponds to III.
Thus, the correct matching is A-II, B-I, C-IV, D-III.