The implied agreement between the people and the government, in which the people give up some of their power and freedom in exchange for protection of their rights what does this definition describe?

The correct answer b) social contract. 
the other answers are wrong, for example: the divine right of king would mean that the king has a right to rule and does need an agreement from the people and natural rights are rights that all people have but the agreement, is not a right, but an agreement, or in other words: contract.