${{\left( \frac{{{3}^{2}}{{.3}^{4}}}{{{6}^{5}}.9} \right)}^{4}}:{{\left( \frac{{{2}^{4}}}{64} \right)}^{12}}$

$={{\left( \frac{{{3}^{2}}{{.3}^{4}}}{{{3}^{5}}{{.2}^{5}}{{.3}^{2}}} \right)}^{4}}:{{\left( \frac{{{2}^{4}}}{{{2}^{6}}} \right)}^{12}}$

$={{\left( \frac{1}{{{3.2}^{5}}} \right)}^{4}}:{{\left( \frac{1}{{{2}^{2}}} \right)}^{12}}$

$=\frac{1}{{{3}^{4}}{{.2}^{20}}}{{.2}^{24}}={{\left( \frac{2}{3} \right)}^{4}}=\frac{16}{81}$