Step 1: Dasharathasya Kulguruh.
The royal preceptor (Kul Guru) of King Dasharatha was Vashishthah.
So, A → III.
Step 2: Bharatasya Patni.
Bharata, the son of Dasharatha, was married to Mandavi.
So, B → I.
Step 3: Ravanasya Mata.
The mother of Ravana was Kaikashi, also known as Kaikeshi.
So, C → IV.
Step 4: Ahilyayah Patih.
The husband of Ahilya was Gautamah, the sage.
So, D → II.
Step 5: Conclusion.
Thus, the correct matching is A - III, B - I, C - IV, D - II.