A man pushes a lawn mower on a level lawn with a force of 200 N. If 40% of this force is directed downward, how much work was done by the man in pushing the mower a horizontal distance of 6.0 m?

Work is equal to the force applied times the distance moved in the direction of that force. It can also be thought of as the distance traveled times the component of force in the direction of travel. So if you know how to break the 200N force into its horizontal and vertical components, you multiply the horizontal component of force times distance traveled.