The correct answer is C) Through tangential slots in the sprayer plate. In an auxiliary boiler return flow fuel oil system, the fuel oil enters the whirling chambers of the sprayer plates through tangential slots. This design creates a swirling motion that atomizes the fuel, allowing for better combustion in the boiler. The tangential slots in the sprayer plate are specifically engineered to achieve this swirling effect. The other options are incorrect because: A) the fuel does not enter through the outer barrel tube, B) the fuel does not enter directly through the drilled passages in the sprayer plate, and D) the fuel does not enter through baffles in the orifice plate. The key design feature is the tangential slots in the sprayer plate that create the desired swirling motion of the fuel.