Step 1: Concept Overview:
The question requires identifying the primary ancient Indian text dedicated to grammar from the given options.
Step 2: Detailed Analysis:
Examining each text:
\[\begin{array}{rl} \bullet & \text{Prashana Upnishada: An Upanishad, part of Hindu philosophical and spiritual literature. Not related to grammar. } \\ \bullet & \text{Ashtadhyayi: Authored by Panini around the 5th century BCE, this text ("Eight Chapters") is the foundational work on Sanskrit grammar, offering a systematic analysis of Sanskrit morphology and phonology. } \\ \bullet & \text{Natyashastra: A comprehensive treatise on performing arts (drama, dance, music) by Bharata Muni. Deals with dramaturgy, not grammar. } \\ \bullet & \text{Meghdoota: A lyric poem by Kalidasa. A literary work, not a grammatical one. } \\ \end{array}\]Therefore, Ashtadhyayi is the ancient grammar text.
Step 3: Conclusion:
The answer is (B).