You may have just added the numerators and then combined the coefficients and added the exponents in the denominators. Instead, find the least common denominator and use this to rewrite each term as an equivalent fraction:

$\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\$

Then simplify and combine the numerators. The correct answer is:

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