\[4\frac{1}{7} \cdot 14 - 1\frac{1}{4} \cdot 1\frac{1}{6} - 1\frac{2}{9} \cdot 2\frac{5}{8} =\]
\[= \frac{29 \cdot 14}{7} - \frac{5 \cdot 7}{4 \cdot 6} - \frac{11 \cdot 21}{9 \cdot 8} =\]
\[= 58 - \frac{35}{24} - \frac{77}{24} =\]
\[= 58 - \frac{112}{24} = 57\frac{24}{24} - 4\frac{16}{24} =\]
\[= 53\frac{8}{24} = 53\frac{1}{3}\]