Choice "D" is correct. Anything having legally recognized value can constitute consideration. If parties legitimately disagree as to the amount owed under their contract, a promise to compromise, such as the parties are doing here, has legal value and constitutes consideration since both parties are giving up the right to litigate the dispute.
Choice "c" is incorrect. A promise to do something that one is already obligated to do has no legal value and is not valid consideration under the preexisting legal duty rule. A police officer has a preexisting legal duty to catch thieves; therefore, this promise cannot serve as consideration.
Choice "a" is incorrect. A promise to do something one is already obligated to do has no value and is not valid consideration under the preexisting legal duty rule. Here, the builder already owed a duty to complete the contract, and so his second promise to do so is not valid consideration.
Choice "b" is incorrect. If parties legitimately disagree as to the amount owed under their contract, a promise to compromise has legal value and constitutes consideration since both parties are giving up the right to litigate the dispute. However, here the amount owed is liquidated, which means that it is not in dispute. A promise to compromise here has no legal value and cannot serve as consideration since there is no legitimate right to litigate a liquidated claim.