Answer
$-4\gt c$

Work Step by Step
$-6\gt c-2$ : add 2 to both sides
$-6+2\gt c-2+2$ : simplify
$-4\gt c$
Verify that -4 is not a solution.
$-6\overset?\gt-4-2$
$-6\ /\!\!\!\!\gt-6\checkmark$
Verify that a number less than -4 is a solution.
$-6\overset?\gt -6-2$
$-6\gt-8\checkmark$