\[\boxed{\mathbf{2.}\mathbf{398}}\]
\[\left( 7 - 6\frac{4}{7} \right) \cdot \left( 4 - 2\frac{1}{4} \right) <\]
\[< 7 \cdot 6\frac{4}{7} - 4 \cdot 2\frac{1}{4}\]
\[1)\ \left( 7 - 6\frac{4}{7} \right) \cdot \left( 4 - 2\frac{1}{4} \right) =\]
\[= \frac{3}{7} \cdot 1\frac{3}{4} = \frac{3}{7} \cdot \frac{7}{4} = \frac{3}{4}\]
\[2)\ 7 \cdot 6\frac{4}{7} - 4 \cdot 2\frac{1}{4} =\]
\[= 7 \cdot \left( 6 + \frac{4}{7} \right) - 4 \cdot \left( 2 + \frac{1}{4} \right) =\]
\[= 42 + 4 - (8 + 1) = 46 - 9 =\]
\[= 37\]