The correct answer is: C) Hinduism.
The Gangas of Talakadu were a Hindu dynasty that ruled over parts of southern India from the 3rd to the 10th centuries CE. During their rule, Hinduism became the dominant religion in the region. This was due in part to the patronage of the Gangas, who built many Hindu temples and promoted the Hindu faith.
Jainism and Buddhism were also present in the region during the rule of the Gangas, but they did not have the same level of influence as Hinduism. This was likely due to the fact that the Gangas were Hindu rulers who supported Hinduism.
Islam did not arrive in India until the 7th century CE, after the death of the Prophet Muhammad. It did not become a major religion in India until the 12th century CE, after the Muslim conquest of northern India. Therefore, it is unlikely that Islam had a significant presence in the region during the rule of the Gangas.
In conclusion, the religion that gained prominence during the rule of the Gangas of Talakadu was Hinduism. This was due in part to the patronage of the Gangas, who built many Hindu temples and promoted the Hindu faith.