The correct answer is (c).
Section 144 of the Code of Criminal Procedure (CrPC) empowers a Magistrate of the first class to issue an order in urgent cases to prevent the commission of cognizable offences or to maintain public order. The order can be for a period of one month, which can be extended by the Magistrate for a further period of one month. However, the state government has the power to further extend the order for a period not exceeding six months.
The options (a), (b), and (d) are incorrect because they are not the maximum period for which the state government has power to further extend the order made by the Magistrate.