2 ≤ |x-6| < 5

Break that into two inequalities:

 2 ≤ x-6 < 5          2 ≤ -(x-6) < 5
+6    +6  +6          2 ≤  -x+6  < 5
------------         -6      -6   -6
 8 ≤ x   < 11        -4 ≤  -x    <-1
                      4 ≥   x    > 1
You might want to write the second one in reverse so it
will go left to right instead or right to left  1 < x ≤ 4

 8 ≤ x < 11,   1 < x ≤ 4



          1 < x ≤ 4,           8 ≤ x < 11
----------○========●-----------○========●---------
-2 -1  0  1  2  3  4  5  6  7  8  9 10 11 12 13 14

Interval notation:    (1,4] U (8,11]     

Edwin