Pushing an empty refrigerator box down an icy path requires overcoming the least amount of kinetic friction.
Kinetic friction is the force that opposes the motion of two surfaces that are sliding against each other. The amount of kinetic friction depends on the materials of the two surfaces and the force pressing them together.
Ice is a very smooth surface, so it has a low coefficient of friction. This means that there is less force of kinetic friction between an object and an icy surface than between an object and a rough surface.
In addition, the weight of the object also affects the amount of kinetic friction. A heavier object has more force pressing it against the surface, so it will have more kinetic friction.
So, pushing an empty refrigerator box down an icy path will require overcoming the least amount of kinetic friction because the ice is a smooth surface and the refrigerator box is relatively light.