Hint The difference between the flat shoe and the high heels on sand is pressure. The pressure is inversely proportional to the area of contact between the different shoes and the sand. Higher pressure creates more deformation than lower pressure shoes.
Complete step by step answer During the process of walking, at a time, a person exerts a force with his or her shoe on the ground which, according to Newton’s third law of motion, exerts an equal and opposite force on the shoe which pushes his legs up and thus have the capability to walk. However, in actuality, the ground is a structure, which can deform under pressure, this deformation is how the ground provides the force required to be exerted back the complete force exerted by the shoe. The deformation is directly proportional to the pressure (not the force) exerted by the shoe. However, concrete is very hard (i.e. the young modulus is high) and does not deform noticeably under the weight of a human. But for loose particles such as sand, mud or soil which do not have a structure, the individual particles do not have enough “strength” to provide the complete force exerted by the shoes of the person hence accelerate downward under their influence, deforming noticeably according to the pressure exerted on it. This downward movement of the particle and hence the shoe reduces the ease of walking. Any structure that allows a large downward movement of the legs when walking reduces the ease of walking such as walking on a trampoline. Since the pressure is inversely proportional to area, hence, wider shoes exert less pressure, thus the less deep it goes. Hence it is easier to walk with flat shoes because the pressure exerted on the ground is lesser than for high heels.
Note For clarity, there's less deformation for lower pressure because there are a larger number particles below the shoe absorbing the force exerted by the shoe, hence, the force required will be achieved earlier than for higher pressure shoes which have a lower number of particles below the shoe.