Explain the relationship between kinetic and potential energy in the example (the pic) while using the words mechanical energy and conservation of energy.

PE is the energy acquired by a body due to its height ! While KE is the energy acquired by the body due to its motion !

KE+PE = mechanical energy and thus mechanical energy is always conserved due to the conservation of energy which states that energy is neither created nor destroyed but only transformed !

As newton's first law states a object in motion stays in motion