Answer
$8$
Work Step by Step
We use one or a combination of theorems (11) to (15).
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Starting with
$D=\left|\begin{array}{lll}{x}&{y}&{z}\\{u}&{v}&{w}\\{1}&{2}&{3}\end{array}\right|$,
multiplying row 3 with 2, we obtain
$D_{1}=\left|\begin{array}{lll}{x}&{y}&{z}\\{u}&{v}&{w}\\{2}&{4}&{6}\end{array}\right|.$
By theorem (14),
If any row (or any column) of a determinant is multiplied by a nonzero number $k,$ the value of the determinant is also changed by a factor of $k.$
$D_{1}=2D=8$
