To answer this question, you need to have knowledge about the history of Tamil Nadu and the dynasties that ruled the region.
Option A) Kakatiyas - This option is incorrect because the Kakatiya dynasty was not one of the four dynasties flourishing in Tamil Nadu. The Kakatiyas were a dynasty that ruled the Deccan region, particularly present-day Telangana and Andhra Pradesh.
Option B) Rashtrakutas - This option is incorrect because the Rashtrakuta dynasty was also not one of the four dynasties flourishing in Tamil Nadu. The Rashtrakutas were a dynasty that ruled parts of central and southern India, including present-day Maharashtra and Karnataka.
Option C) Pallavas - This option is correct. The Pallava dynasty was one of the four dynasties flourishing in Tamil Nadu. They ruled the region from the 3rd century CE to the 9th century CE and were known for their patronage of art, architecture, and literature.
Option D) Hoysalas - This option is incorrect because the Hoysala dynasty was also not one of the four dynasties flourishing in Tamil Nadu. The Hoysalas were a dynasty that ruled parts of present-day Karnataka.
The correct answer is C) Pallavas. They were one of the four dynasties flourishing in Tamil Nadu.