\[2\frac{7}{15} - \left( 2\frac{2}{15} - 8\frac{1}{9} \right) =\]
\[= 2\frac{7}{15} - 2\frac{2}{15} + 8\frac{1}{9} = \frac{5}{15} + 8\frac{1}{9} =\]
\[= \frac{1}{3} + 8\frac{1}{9} = \frac{3}{9} + 8\frac{1}{9} = 8\frac{4}{9}.\]