Change subtraction to addition of the opposite: $\displaystyle{\left({4}{{m}}^{{3}}+{6}\right)}+{\left({2}{{m}}^{{3}}-{{m}}^{{2}}-{3}\right)}\usepackage{cmbright}\Huge\$

Regroup to match like terms: $\displaystyle{\left({4}{{m}}^{{3}}+{2}{{m}}^{{3}}\right)}+{\left(-{{m}}^{{2}}\right)}+{\left({6}+-{3}\right)}\usepackage{cmbright}\Huge\$

Combine like terms: $\displaystyle{6}{{m}}^{{3}}-{{m}}^{{2}}+{3}\usepackage{cmbright}\Huge\$