Question 136843
You are on the right track.

Plug in (x-2) in all the places where x was.

{{{g(x-2) = 2(x-2)^2-2(x-2)-4}}}
{{{g(x-2) = 2(x^2-4x+4) - 2x+4 - 4}}}
{{{g(x-2) = 2x^2 -8x +8 - 2x }}}
{{{g(x-2) = 2x^2 -10x +8 }}}  some folks would be OK with this answer
{{{g(x-2) = 2x^2 - 2x - 4 -8x + 12}}}
{{{g(x-2) = g(x) - 8x + 12}}} other folks would want you to state in terms of g(x)