So if 6 dozen cookies needs 3/4 cup of sugar, and we need to know how much sugar is needed to make 4 dozen, then find how much of 6 dozen 4 dozen is.
To do this, put it as a fraction:
4 dozen / 6 dozen, or 4/6, which is 2/3.
Since conveniently it calls for 3/4 cup of sugar, we can multiply that by 2/3, and we'll get 6/12, or 1/2.
So 1/2 cup of sugar is needed for 4 dozen cookies.