The given function is
[tex]g(x)=6x^2-2x+9[/tex]We need to find the derivative of g(x), then
[tex]\begin{gathered} g^{\prime}(x)=6(2)x^{2-1}-2(1)x^{1-1}+0 \\ g^{\prime}(x)=12x^1-2x^0 \end{gathered}[/tex]Remember any variable to the power of 0 = 1
[tex]g^{\prime}(x)=12x-2[/tex]We need to find the derivative at x = -2, then substitute x by -2 in g'(x)
[tex]\begin{gathered} g^{\prime}(-2)=12(-2)-2 \\ g^{\prime}(-2)=-24-2 \\ g^{\prime}(2)=-26 \end{gathered}[/tex]The derivative of g(x) at x = -2 is -26