To reduce the power output of an engine equipped with a constant-speed propeller, what should be done first?

To effectively reduce the power output of an engine equipped with a constant-speed propeller, the first step is to reduce manifold pressure with the throttle control. This is because the throttle directly controls the amount of air and fuel mixture entering the engine. By reducing the manifold pressure, you decrease the engine's power output since the engine experiences less load and operates at a lower power setting.

In this context, adjusting the throttle is the most immediate and appropriate method for controlling engine power without shutting down the engine or making more drastic changes. As the manifold pressure decreases, the engine's performance adjusts accordingly, allowing the propeller to maintain its speed while producing less thrust.

Other options, such as reducing RPM with propeller control, may not be the first priority since the goal is to manage power output during normal operation. Shutting down the engine would be an extreme measure and not practical for simply reducing power during flight operations. Increasing fuel flow would have the opposite effect, potentially increasing power output rather than reducing it. Thus, reducing manifold pressure through throttle control is the best initial action to take.