The correct answer is C) follow-up control. In an electro-hydraulic steering system, the follow-up control mechanism is responsible for maintaining close synchronization between the steering wheel position and the actual movement of the rudder. The follow-up control continuously monitors the position of the steering wheel and the position of the rudder, and makes adjustments to the hydraulic system to ensure that the rudder movement matches the steering wheel input. This ensures precise and responsive steering control. The other answer choices are incorrect because: A) the six-way valve is responsible for directing the hydraulic fluid flow, but does not directly control the synchronization; B) the Rapson slide is a mechanical linkage used in some steering systems, but not in electro-hydraulic systems; and D) the "trick wheel" is not a component of an electro-hydraulic steering system.