You Place A Box Weighing 220.4 N On An Inclined Plane That Makes A 38.6◦ Angle With The Horizontal. Compute The Component Of The Gravitational Force Acting Down The Inclined Plane. Answer In Units Of N?

The force acting parallel to the surface of the plane is the sine of the angle of elevation times the force acting "down."
  220.4*sin[38.6°] = 220.4*0.6 = 132.24

Your force is 132.24 N down the plane.