which number line represents the solutions to -2|x| = -6?

Explanation:

Step1: Isolate the absolute - value expression

Divide both sides of the equation $-2|x|=-6$ by $-2$. We get $|x| = 3$.

Step2: Solve the absolute - value equation

The absolute - value equation $|x| = 3$ has two solutions. When $x\geq0$, $|x|=x$, so $x = 3$. When $x\lt0$, $|x|=-x$, so $-x = 3$, which gives $x=-3$.

Answer:

The number line with points at $x = - 3$ and $x = 3$ (the second option from the top if we assume the order of the number - lines as presented in the image).