Step 1: Pailah.
Pailah, a disciple of Vyasa, is associated with the Rigveda. Therefore, A corresponds to III.
Step 2: Jaiminih.
Jaiminih, a disciple of Vyasa, is associated with the Yajurveda. Therefore, B corresponds to I.
Step 3: Vaishampayanah.
Vaishampayanah is linked with the Samaveda. Therefore, C corresponds to IV.
Step 4: Sumantuh.
Sumantuh was associated with the Atharvaveda. Therefore, D corresponds to II.
Step 5: Conclusion.
The correct matching is A - III, B - I, C - IV, D - II.