\[4\frac{1}{8} - 6\frac{2}{9} + \left( - 3\frac{1}{6} \right) - \left( - 5\frac{3}{4} \right) =\]
\[= 4\frac{9}{72} - 6\frac{16}{72} - 3\frac{12}{72} + 5\frac{54}{72} =\]
\[= \left( 4\frac{9}{72} + 5\frac{54}{72} \right) - \left( 6\frac{16}{72} + 3\frac{12}{72} \right) =\]
\[= 9\frac{63}{72} - 9\frac{28}{72} = \frac{35}{72}\]