Answer
48 cubic units.
Work Step by Step
The volume of the parallelepiped is given as:
$|\textbf{u}\cdot (\textbf{v}\times\textbf{w})|$
We calculate the dot product and cross product as follows:
$\textbf{u}\cdot (\textbf{v}\times\textbf{w})$= det $\begin{pmatrix}u\\v\\w\end{pmatrix}$
$=\begin{vmatrix}1&2&6\\1&3&-2\\2&-1&4\end{vmatrix}$
$=1(3\times4-(-1\times-2))-2(1\times4-2\times-2)+6(1\times-1-2\times3)$
$=10-16-42=-48$
Volume= $|\textbf{u}\cdot (\textbf{v}\times\textbf{w})|=48$
