Hello! 12 make a dozen. 12 * 6 is 72. 72 cookies make 6 dozen. 2 cups of sugar are needed to make 6 dozen. 36 cookies is 3 dozen, because 3 * 12 is 36. 36 is ½ of 72, so we would need ½ of the amount of sugar needed for 6 dozen cookies for 3 dozen cookies. ½ of 2 is 1. There. 1 cup of sugar is needed to make 3 dozen cookies.