The correct answer is C) decrease to a slightly lower value. If the speeder spring of a main propulsion diesel engine governor breaks while operating at full load, the engine RPM will decrease to a slightly lower value. This is because the governor is responsible for maintaining a constant engine speed by adjusting the fuel supply. When the speeder spring breaks, the governor's ability to control the engine speed is compromised, causing the engine RPM to decrease slightly from the desired set point. The other options are incorrect. Option A is incorrect because the engine RPM will not hunt until stabilized by the droop rod, as the governor's control is impaired. Option B is incorrect because the engine RPM will not increase until the overspeed trip is actuated, as the governor is unable to increase the fuel supply to maintain the set speed. Option D is incorrect because the engine RPM will not remain the same, as the governor's function is disrupted by the broken speeder spring.