|x-15| - |x-9| = -6

First, simplify each absolute value expression:

|x-15| = |-(x-15)| = |-x+15| = x-15

|x-9| = |-(x-9)| = |-x+9| = x-9

Now substitute back into the original equation:

x-15 - (x-9) = -6
x-15 - x + 9 = -6
-6 = -6

Therefore, the equation holds true for all real numbers x.