Answer
See the picture below.
Work Step by Step
The parent function is $f(x)=\vert x\vert$ (with red), but the graph of $g(x)=-2\vert x\vert$ (with blue) will be narrower, as the coefficient multplies each y-value of the parent function by $2$ and will also be reflected across the x-axis because of the coefficient of $-1$.
For drawing the exact graph of the parent function here is a table of values:
$f(-2)=\mid -2\mid=2$
$f(-1)=\mid -1\mid=1$
$f(0)= \mid 0\mid=0$
$f(1)= \mid 1\mid=1$
$f(2)= \mid 2\mid=2$
By the use of graph transformation techniques, the graph is stretched by a factor of $2$ and will also be reflected across the x-axis.
For drawing the exact graph of $g(x)$ here is the table of values of the given function:
$g(-2)=-2 \mid -2\mid=-4$
$g(-1)=-2 \mid -1\mid=-2$
$g(0)=-2 \mid 0\mid=0$
$g(1)=-2 \mid 1\mid=-2$
$g(2)=-2 \mid 2\mid=-4$
