Rules for getting rid of absolute values:

If A is a POSITIVE number:

|EXPRESSION| < A becomes this--->    -A < EXPRESSION < A

|EXPRESSION| > A becomes this--->    EXPRESSION < -A OR EXPRESSION > A

So:

|c-2| > 6  becomes this--->  c-2 < -6 OR c-2 > 6 
add 2 to both sides in each:   c < -4 OR   c > 8

so the graph of the solution is this number line:

 <=======o-----------------------------------o======>
  -7 -6 -4 -3 -2 -1  0  1  2  3  4  5  6  7  8  9 10

And the interval notation for that is:
   
                    (-oo, -4) U (8, oo)              

*****************************************************
*****************************************************

|3-(x-1)| < 8  becomes this:   -8 < 3-(x-1) < 8   
remove parentheses:            -8 <  3-x+1  < 8
combine 3 and +1 :             -8 <   2-x   < 8
subtract 2 from all 3 sides:  -10 <    -x   < 6
divide thru by -1 which
reverses the < to > :          10 >     x   > 6
that is now greatest to smallest
which can be written smallest
to greatest:                       6 < x < 10

The graph is on this number line:

----------------------o===========o------------
-1  0  1  2  3  4  5  6  7  8  9 10 11 12 13 14

which in interval notation is  (6, 10)

Note:  (6, 10) looks like a point on an xy-axis,
but it isn't.  We have to go by context to determine
whether (6, 10) represents an interval notation or
a point like (x, y).  Here it is interval notation.

Edwin