If \([\bar{a} \quad \bar{b} \quad \bar{c}]=4\), then volume of parallelopiped with coterminus edges \(\bar{a}+2 \bar{b}\),
\(\bar{b}+2 \bar{c}, \quad \bar{c}+2 \bar{a}\) is

Given \(\bar{a} \cdot(\bar{b} \times \bar{c})=4\)
\(\therefore\) Volume of parallelopiped
\(\begin{array}{l}
=(\overline{\mathrm{a}}+2 \overline{\mathrm{b}}) \cdot[(\overline{\mathrm{b}}+2 \overline{\mathrm{c}}) \times(\overline{\mathrm{c}}+2 \overline{\mathrm{a}})] \\
=(\overline{\mathrm{a}}+2 \overline{\mathrm{b}}) \cdot[(\overline{\mathrm{b}} \times \overline{\mathrm{c}})+2(\overline{\mathrm{b}} \times \overline{\mathrm{a}})+2(\overline{\mathrm{c}} \times \overline{\mathrm{c}})+4(\overline{\mathrm{c}} \times \overline{\mathrm{a}})] \\
=[\overline{\mathrm{a}} \cdot(\overline{\mathrm{b}} \times \overline{\mathrm{c}})]+[2 \overline{\mathrm{a}} \cdot(\overline{\mathrm{b}} \times \overline{\mathrm{a}})]+[4 \overline{\mathrm{a}} \cdot(\overline{\mathrm{c}} \times \overline{\mathrm{a}})]+ \\
=[2 \overline{\mathrm{b}} \cdot(\overline{\mathrm{b}} \times \overline{\mathrm{c}})]+[4 \overline{\mathrm{b}} \cdot(\overline{\mathrm{b}} \times \overline{\mathrm{a}})]+[8 \overline{\mathrm{b}} \cdot(\overline{\mathrm{c}} \times \overline{\mathrm{a}})] \\
=[\overline{\mathrm{a}} \cdot(\overline{\mathrm{b}} \times \overline{\mathrm{c}})]+0+[8 \overline{\mathrm{b}} \cdot(\overline{\mathrm{c}} \times \overline{\mathrm{a}})] \\
=9[\overline{\mathrm{a}} \cdot(\overline{\mathrm{b}} \times \overline{\mathrm{c}})]=9(4)=36
\end{array}\)