9 = 6 + |s-3|

Isolate the absolute value term on the right by subtracting 6 
from both sides

                3 = |s-3|

Since the two equations " 3 = |3| " and " 3 = |-3| " are both true, we have to
make two equations, one for each case that the thing inside the absolute value
bars s-3, is either equal to 3 or to -3:

         s-3 = 3     s-3 = -3

Add 3 to each side of both equations:

           s = 6       s = 0

There are usually two solutions for an absolute value equation.  But you might
get extraneous solutions, so you'd better check them.

Checking s = 6

             9 = 6 + |s-3|
             9 = 6 + |6-3|
             9 = 6 + |3|
             9 = 6 + 3
             9 = 9

Checking s = 0

             9 = 6 + |s-3|
             9 = 6 + |0-3|
             9 = 6 + |-3|
             9 = 6 + 3
             9 = 9

They both check.                 

Edwin