Rewrite each term as an equivalent fraction using the LCD, which is $\displaystyle{36}{{m}}^{{6}}\usepackage{cmbright}\Huge\$ :

$\displaystyle\frac{{4}}{{{9}{{m}}^{{2}}}}-\frac{{{{n}}^{{2}}}}{{{6}{{m}}^{{4}}}}+\frac{{{5}{n}}}{{{12}{{m}}^{{6}}}}=\frac{{{4}{\left({4}{{m}}^{{4}}\right)}}}{{{\left({9}{{m}}^{{2}}\right)}{\left({4}{{m}}^{{4}}\right)}}}-\frac{{{{n}}^{{2}}{\left({6}{{m}}^{{2}}\right)}}}{{{\left({6}{{m}}^{{4}}\right)}{\left({6}{{m}}^{{2}}\right)}}}+\frac{{{5}{n}{\left({3}\right)}}}{{{\left({12}{{m}}^{{6}}\right)}{\left({3}\right)}}}\usepackage{cmbright}\Huge\$

$\displaystyle=\frac{{{16}{{m}}^{{4}}}}{{{36}{{m}}^{{6}}}}-\frac{{{6}{{m}}^{{2}}{{n}}^{{2}}}}{{{36}{{m}}^{{6}}}}+\frac{{{15}{n}}}{{{36}{{m}}^{{6}}}}=\frac{{{16}{{m}}^{{4}}-{6}{{m}}^{{2}}{{n}}^{{2}}+{15}{n}}}{{{36}{{m}}^{{6}}}}\usepackage{cmbright}\Huge\$