Factor the numerators and denominators. Regroup common factors in the same fraction and reduce to 1. Multiply simplified expressions.

$\displaystyle\frac{{{30}{{a}}^{{3}}}}{{{{a}}^{{2}}-{16}}}\cdot\frac{{{{a}}^{{2}}+{4}{a}}}{{{24}{{a}}^{{3}}}}=\frac{{{6}\cdot{5}\cdot{{a}}^{{3}}}}{{{\left({a}+{4}\right)}{\left({a}-{4}\right)}}}\cdot\frac{{{a}\cdot{\left({a}+{4}\right)}}}{{{6}\cdot{4}\cdot{{a}}^{{3}}}}\usepackage{cmbright}\Huge\$

$\displaystyle=\frac{{{6}\cdot{{a}}^{{3}}\cdot{\left({a}+{4}\right)}}}{{{6}\cdot{{a}}^{{3}}\cdot{\left({a}+{4}\right)}}}\cdot\frac{{{5}}}{{{\left({a}-{4}\right)}}}\cdot\frac{{a}}{{4}}={1}\cdot\frac{{{5}\cdot{a}}}{{{4}{\left({a}-{4}\right)}}}=\frac{{{5}{a}}}{{{4}{a}-{16}}}\usepackage{cmbright}\Huge\$