Correct. Factor both terms, find their GCF, and factor it out of the expression.

$\displaystyle{18}{{a}}^{{4}}{{b}}^{{2}}={2}\cdot{3}\cdot{3}\cdot{a}\cdot{a}\cdot{a}\cdot{a}\cdot{b}\cdot{b}\usepackage{cmbright}\Huge\$

$\displaystyle{30}{{a}}^{{2}}{{b}}^{{3}}={2}\cdot{3}\cdot{5}\cdot{a}\cdot{a}\cdot{b}\cdot{b}\cdot{b}\usepackage{cmbright}\Huge\$

GCF $\displaystyle={2}\cdot{3}\cdot{a}\cdot{a}\cdot{b}\cdot{b}={6}{{a}}^{{2}}{{b}}^{{2}}\usepackage{cmbright}\Huge\$

$\displaystyle{18}{{a}}^{{4}}{{b}}^{{2}}+{30}{{a}}^{{2}}{{b}}^{{3}}={6}{{a}}^{{2}}{{b}}^{{2}}{\left({3}{{a}}^{{2}}\right)}+{6}{{a}}^{{2}}{{b}}^{{2}}{\left({5}{b}\right)}={6}{{a}}^{{2}}{{b}}^{{2}}{\left({3}{{a}}^{{2}}+{5}{b}\right)}\usepackage{cmbright}\Huge\$

The missing exponent is 2.