Option 1: Peshwa - The Peshwa was the prime minister and chief advisor to the king. Their role was mainly administrative and they were responsible for overseeing the day-to-day functioning of the government. However, the Peshwa did not hold the charge of finance in Shivaji`s council.

Option 2: Amatya - Amatya was the minister who held the charge of finance in Shivaji`s council. They were responsible for managing the finances of the kingdom, including collecting taxes, overseeing budgets, and making financial decisions.

Option 3: Sumant - Sumant was responsible for foreign affairs and diplomacy in Shivaji`s council. They handled negotiations with other kingdoms and managed relations with foreign powers. They did not hold the charge of finance.

Option 4: Pandit Rao - The role of Pandit Rao in Shivaji`s council is not clear. There is no evidence to suggest that Pandit Rao held the charge of finance.

Therefore, based on the given options, the correct answer is Option 2: Amatya. Amatya was the minister in the eight-member council of Shivaji who held the charge of finance.