Incorrect. First write the quotient as a fraction:

$\displaystyle\frac{{f{{\left({x}\right)}}}}{{g{{\left({x}\right)}}}}=\frac{{{12}{{x}}^{{3}}+{6}{{x}}^{{2}}}}{{{3}{{x}}^{{2}}}}\usepackage{cmbright}\Huge\$

Factor the numerator and simplify.