The correct answer is Gautama.
Gautama is the author of the Nyaya Sutra, a foundational text of the Nyaya school of Hindu philosophy. The Nyaya Sutra is a systematic treatise on logic and epistemology, and it is one of the most important texts in the history of Indian philosophy.
Vyasa is the author of the Mahabharata, one of the longest epic poems in the world. He is also credited with compiling the Vedas, the sacred texts of Hinduism.
Kapila is the founder of the Samkhya school of Hindu philosophy. The Samkhya school is a dualistic philosophy that posits the existence of two fundamental principles: Purusha (consciousness) and Prakriti (matter).
Charaka is the author of the Charaka Samhita, an ancient Indian medical text. The Charaka Samhita is one of the most important texts in the history of Indian medicine.
Gautama, Vyasa, Kapila, and Charaka are all important figures in Indian history and philosophy. However, only Gautama is the author of the Nyaya Sutra.