Ответ:

\(16-6\frac23\cdot\left(37\frac45:12-20:7\frac19\right)=16-\frac{20}{3}\cdot\left(\frac{189}{5}:12-20:\frac{64}{9}\right)\).

\(=16-\frac{20}{3}\cdot\left(\frac{63}{20}-\frac{45}{16}\right)=16-\frac{20}{3}\cdot\frac{27}{80}=16-\frac94=13\frac34\).

Ответ: \(13\frac34\).