#### Answer

$\underset{x\to -2}{\mathop{\lim }}\,\left| 2x \right|=4$, since, as x approaches $-2$ the value of $ f\left( x \right)$ gets closer to the y-coordinate of 4.

#### Work Step by Step

Consider the provided limit $\underset{x\to -2}{\mathop{\lim }}\,\left| 2x \right|$.
To find $\underset{x\to -2}{\mathop{\lim }}\,\left| 2x \right|$ examine the portion of the graph near $ x=-2$.
As x approaches $-2$ the value of $ f\left( x \right)$ gets closer to the y-coordinate of $4$. This point $\left( -2,4 \right)$ is shown by the solid dot in the above graph.
The point $\left( -2,4 \right)$ has a y-coordinate of $4$.
Thus, $\underset{x\to -2}{\mathop{\lim }}\,\left| 2x \right|=4$.
Hence, the value of $\underset{x\to -2}{\mathop{\lim }}\,\left| 2x \right|$ is 4.