To subtract polynomials, remove the parentheses, change the signs of the terms of the second polynomial, regroup, and then combine like terms.

$\displaystyle{12}{{m}}^{{2}}-{6}{m}{n}-{9}{{n}}^{{2}}+{4}{{n}}^{{2}}+{6}{m}{n}-{14}{{m}}^{{2}}={12}{{m}}^{{2}}-{14}{{m}}^{{2}}-{6}{m}{n}+{6}{m}{n}-{9}{{n}}^{{2}}+{4}{{n}}^{{2}}=-{2}{{m}}^{{2}}-{5}{{n}}^{{2}}\usepackage{cmbright}\Huge\$