Step 1: King Dasharatha's Royal Preceptor.
King Dasharatha's Kul Guru was Vashishthah.
Therefore, A corresponds to III.
Step 2: Bharata's Wife.
Bharata, Dasharatha's son, was married to Mandavi.
Therefore, B corresponds to I.
Step 3: Ravana's Mother.
Ravana's mother was Kaikashi, also known as Kaikeshi.
Therefore, C corresponds to IV.
Step 4: Ahilya's Husband.
Ahilya's husband was the sage Gautamah.
Therefore, D corresponds to II.
Step 5: Final Arrangement.
Hence, the correct matching is A - III, B - I, C - IV, D - II.