Be careful to subtract in the correct order. Start with:

$\displaystyle{f{{\left({x}\right)}}}-{g{{\left({x}\right)}}}={2}{{x}}^{{3}}-{4}{x}+{6}-{\left({2}{{x}}^{{3}}+{3}{{x}}^{{2}}-{4}{x}+{2}\right)}\usepackage{cmbright}\Huge\$

Distribute the minus sign to all terms of the second function and then combine like terms.