The factored form of $\displaystyle{64}{{x}}^{{9}}-{27}{{y}}^{{6}}\usepackage{cmbright}\Huge\$ is shown. Find the value of the missing exponent.

$\displaystyle{64}{{x}}^{{9}}-{27}{{y}}^{{6}}={\left({4}{{x}}^{{3}}-{3}{{y}}^{{2}}\right)}{\left({16}{{x}}^{{6}}+{12}{{x}}^{{3}}{{y}}^{{2}}+{9}{{y}}^{?}\right)}\usepackage{cmbright}\Huge\$