idhma-vāhātmajo muniḥ

agastyah-the great sage Agastya Muni; prak-first; duhitaram-daughter; upayeme-married; dhrta-vratam-taken to vows; yasyam-through whom; drdha-cyutah-named Drdhacyuta; jatah-was born; idhma-vaha-named Idhmavaha; atma-jah-son; munih-the great sage.