Answer
$12x^2+12xh^2+4h^2-2$
Work Step by Step
$\frac{f(x+h)-f(x)}{h}=\frac{(4(x+h)^3-2(x+h))-(4x^3-2x)}{h}=\frac{(4(x^3+3x^2h+3xh^3+h^3)-2x-2h))-4x^3+2x}{h}=\frac{4x^3+12x^2h+12xh^3+4h^3-2x-2h-4x^3+2x}{h}=\frac{12x^2h+12xh^3+4h^3-2h}{h}=12x^2+12xh^2+4h^2-2$
