Which of the following is a result of shifting a circle with equation(x - 32 (y - 52 = 36 down 2 units?

When you shift down you change the number in parentheses with the y. These up and down changes in the parentheses are always the opposite sign. Positive goes left with the x and down with the y. So subtract 2 from the number with the y. -52 - 2 = -54. So the answer using your notation is (x-32 (y-54 = 36.