\[\boxed{\mathbf{1145}\mathbf{.}\mathbf{\ }}\]
\[\frac{12}{19} \cdot \left( 1\frac{7}{12} \cdot 4\frac{13}{21} \right) =\]
\[= \frac{12}{19} \cdot \frac{19}{12} \cdot \frac{97}{21} = \frac{12 \cdot 19 \cdot 97}{19 \cdot 12 \cdot 21} =\]
\[= \frac{97}{21} = 4\frac{13}{21}\]