Question 163518
You're wrong, but you're on the right track.

{{{f(x+h)=3(x+h)^2-2}}} is correct.
But
{{{(x+h)^2=x^2+2xh+h^2}}}
So then,
{{{f(x+h)=3(x+h)^2-2}}}
{{{f(x+h)=3(x^2+2xh+h^2)-2}}}
{{{f(x+h)=3x^2+6xh+3h^2-2}}}