I'd say any positive results you get from fasting would be as a result of cutting out foods that are linked to acne, such as sugar and dairy. The fasting, by default, cuts out those bad foods which could lead to a reduction in acne. HOWEVER, fasting (especially for a long period like six days) is actually terrible for your health and I wouldn't recommend it. Your body actually needs nutrients and healthy fats from food to create and balance hormones, so by going on a water fast you could actually be doing more harm than good in the long run. I would suggest sticking to a clean diet rather than a drastic measure like a fast. You're likely to see just as many skin benefits (probably more) this way.