\[4\frac{1}{7} \cdot 14 - 2\frac{1}{4} \cdot 3\frac{1}{6} - 1\frac{1}{9} \cdot 3\frac{3}{8} =\]
\[= \frac{29 \cdot 14}{7} - \frac{9 \cdot 19}{4 \cdot 6} - \frac{10 \cdot 27}{9 \cdot 8} =\]
\[= \frac{29 \cdot 2}{1} - \frac{3 \cdot 19}{4 \cdot 2} - \frac{5 \cdot 3}{1 \cdot 4} =\]
\[= 58 - \frac{57}{8} - \frac{15^{\backslash 2}}{4} =\]
\[= 58 - \frac{57 + 15 \cdot 2}{8} =\]
\[= 58 - \frac{57 + 30}{8} = 58 - \frac{87}{8} =\]
\[= 58 - 10\frac{7}{8} = 47\frac{1}{8}.\]