Answer
$f(a) = 3a^2+2 $
$f(a +h)=3a^2+6ah+3h^2 +2 $
$\frac{f(a+h)-f(a)}{h}= 6a+3h$
Work Step by Step
$f(a) =3a^2+2 $
$f(a +h)=3(a+h)^2+2$ ... simplify
$=3(a^2+2ah+h^2)+2$
$=3a^2+6ah+3h^2 +2 $
$\frac{f(a+h)-f(a)}{h}=\frac{(3a^2+6ah+3h^2+2)-(3a^2+2)}{h}$ ... simplify
$=\frac{3a^2+6ah+3h^2+2-3a^2-2}{h}$
$=\frac{6ah+3h^2}{h}$
$=6a+3h$