A pastry chef is making brownies but is running out of butter.  The recipe he is following calls for 2 ounces of butter for every 1 cup of baking mix; however, it allows 2 ounces of coconut oil to be substituted for the 2 ounces of butter if necessary.  The chef would like to use as much butter as possible before switching over and substituting coconut oil.  If the chef had 4 ounces of butter remaining, and he plans on using 6 cups of baking mix, how many ounces of coconut oil will he end up using?
Work out the solution step by step.