The correct answer is C. Patna.
Sher Shah Suri was a Pashtun warrior who founded the Suri Empire in the 16th century. He was born in Sasaram, Bihar, in 1486. He started his career as a soldier in the Mughal army, but he later rebelled against the Mughal emperor Humayun. He defeated Humayun in the Battle of Chausa in 1539 and captured Delhi. He then declared himself the emperor of India.
Sher Shah Suri ruled for only five years, but he made a significant impact on Indian history. He built a number of roads and bridges, and he also introduced a new coinage system. He died in 1545, and his empire collapsed soon after his death.
The other options are incorrect. Gaya is a city in Bihar, but it was not the headquarters of Sher Shah Suri. Darbhanga is also a city in Bihar, but it was not the headquarters of Sher Shah Suri. Saran is a district in Bihar, but it was not the headquarters of Sher Shah Suri.