The main idea behind the concept of work as a physics entity is that it is a force through (times) a net displacement. So, if you were to shove a table around the room and end up in the exact same spot, you would have done no work in the physics sense even though you might be exhausted. That is, since there has been no net displacement, the work done is zero.
Since there is no force involved in (ideal) horizontal movement when one is only considering work done against gravity (think of moving something horizontally about a frictionless surface), one doesn't consider horizontal movement in problems of this type, only vertical movement. So how far did the case (ideally considered as a point starting at zero vertical displacement) move vertically in going up the ramp? What was the force used? [remember F = m a] The work done then is the force times the net vertical displacement.
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