How can I calculate the amount of work done when moving a 567N crate a distance of 20 meters?
If, on the other hand, you lift the crate up 20 meters then you did work according to Work = Force x Distance or W = 567n x 20m = 11340 nm = 11340 Joules. This is because you increased the crate's potential energy from 0 Joules on the floor to PE= mgh = 11340 joules on the shelf.
Note that weight = mass x accel of grav, or w = mg. Since PE=W=mgh, it is also true that W = wh, where height (h) is the distance you lifted it.