She has 9/8 cups of brown sugar as a fraction. As a decimal, which is easier to work with here, it is 1.125. She needs 1.5 cups. If we set this up as a proportion, we can figure out how many cookies she can make meeting the restriction of brown sugar, and then scale the other ingredients down accordingly. To figure the number of cookies, our proportion will have brown sugar on top and number of cookies on bottom. What we are looking for is the number of cookies she can make with 1.125 cups of brown sugar when she can make 24 with 1.5 cups of brown sugar. 
. Cross multiply to get 1.5x = 27 and x = 18. She can make 18 cookies. Now let's backtrack to the ingredients based on the number of cookies we can make. Set each ingredient up in a proportion with the ingredient on top and the number of cookies on the bottom. First ingredient you want is flour. 2.25 cups of flour make 24 cookies and we need to find out how much flour will we need to make 18 cookies. 
. Cross multiply to get 24x = 40.5 which simplifies to x = 27/16 or 1 11/16 cups of flour. Do all the ingredients in the same way and you'll be fine!