\[\boxed{\mathbf{4.}\mathbf{24}}\]
\[\textbf{а)}\ 4\frac{5}{7} \cdot \left( 0,5 - \frac{1}{2} \right) = 4\frac{5}{7} \cdot 0 = 0\]
\[\textbf{б)}\ 4\frac{8}{9} \cdot (0,7 + 0,3) = 4\frac{8}{9} \cdot 1 =\]
\[= 4\frac{8}{9}\]
\[\textbf{в)}\ 4,31 \cdot \left( 6\frac{7}{8} - 5\frac{7}{8} \right) =\]
\[= 4,31 \cdot 1 = 4,31\]
\[\textbf{г)}\ \left( 9,6 - 9\frac{3}{5} \right) \cdot 107\frac{4}{99} =\]
\[= 0 \cdot 107\frac{4}{99} = 0\]