Correct. Multiply each term in the first polynomial with each term in the second polynomial, and then combine the like terms.

$\displaystyle{6}{m}{\left({3}{{m}}^{{2}}\right)}+{6}{m}{\left({5}{m}\right)}+{6}{m}{\left({8}\right)}-{5}{\left({3}{{m}}^{{2}}\right)}-{5}{\left({5}{m}\right)}-{5}{\left({8}\right)}\usepackage{cmbright}\Huge\$

$\displaystyle={18}{{m}}^{{3}}+{30}{{m}}^{{2}}+{48}{m}-{15}{{m}}^{{2}}-{25}{m}-{40}={18}{{m}}^{{3}}+{15}{{m}}^{{2}}+{23}{m}-{40}\usepackage{cmbright}\Huge\$