Can you explain the Work-Energy principle and how you can apply it in a simple situation such as a box sliding down a rough slope?

The Work-Energy principle states that the total work done on or by an object is equal to the total change in energy between the given initial and final states. This can be reworded to also say that the total loss in energy of an object is due to the work done by the external force, e.g. friction. We can also say that the gain in energy of the object is due to the work done by an external force, e.g. someone pushing the object or a source of thrust like an engine. This principle is a step forward from the principle of conservation of energy, in which we learn that the total energy is conserved, but may change form from kinetic to gravitational, elastic etc. In that principle, we are working in a closed environment where external forces don't effect the object. In a real world, such a scenario is impossible, and we need to consider how external forces influence the behaviour, hence the work-energy principle.

In the case of the example in the question, the box begins at rest and at a given height. As it slides down the rough slope, the friction force does work against the motion of the box. The gravitational potential energy (GPE) the box has converts to kinetic energy. In a closed system, all the GPE would convert to kinetic energy. However due to the external friction force, some energy is dissipated (e.g. as heat). The total energy 'lost' at the end is equal to the work done by friction, which is what the work-energy principle states.