If there was 20% antifreeze in 9 quarts of solution, then there 0.8 x 9 quarts of water (7.2 quarts). As you are adding only antifreeze, the amount of water doesn't change. So, you can say that the amount of water in the old solution is equal to the amount of water in the new solution. If V is the volume of the new solution and the amount of water doesn't change, 0.8 x 9 = 0.4 x V. Solve for V to get the total volume of the new solution. This turns out to be 18 quarts. As the old volume was 9 quarts and only antifreeze was added, the difference between 18 quarts and 9 quarts must be the volume of antifreeze added. This assumes that the volumes of water and antifreeze are additive, meaning that one volume of water plus one volume of antifreeze gives two volumes of solution.