Answer
Interval Notation : $[0,12]$
Graph:
Work Step by Step
$|x-6| - 7 \leq -1$
To isolate an absolute value, add $7$ to both sides.
$|x-6| - 7 +7 \leq -1+7 $
$|x-6| \leq 6$
By the absolute value inequality property, this is equivalent to
$-6 \leq x-6 \leq 6$
Add $6$ to all parts,
$-6+6 \leq x-6+6 \leq 6+6$
$0\leq x \leq 12 $
Interval Notation :$[0,12]$