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