Answer
$6x+3h-2.$
Work Step by Step
RECALL: $\\\\$The difference quotient of a function $f$ is given by the formula $\dfrac{f(x+h)-f(x)}{h}$ where $h \ne0$. Use the difference quotient formula above to obtain:
$\dfrac{f(x+h)-f(x)}{h}\\=\dfrac{3(x+h)^2-2(x+h)+6-(3x^2-2x+6)}{h}\\=\dfrac{3x^2+6xh+3h^2-2x-2h+6-3x^2+2x-6}{h}\\=\dfrac{6xh+3h^2-2h}{h}\\=6x+3h-2.$
