Which system is responsible for operating the main landing gear on the C-17?

The correct choice indicates that Hydraulic System No. 3 is responsible for operating the main landing gear on the C-17. This system's primary function includes actuating the gear retraction and extension, which is crucial for safe takeoffs and landings. Hydraulic System No. 3 is specifically designed to support landing gear operations, ensuring that they function reliably during all phases of flight.

Understanding the purpose of the other hydraulic systems is helpful for context. Each hydraulic system on the C-17 has designated roles, such as operating flight control surfaces or supporting auxiliary systems, which showcases the importance of having multiple hydraulic systems for redundancy and specialized functions. In emergencies or failures, backup systems can take over essential operations, but in this specific case, it is Hydraulic System No. 3 that directly handles the main landing gear.