To solve the equation -2|x| = 4, we can start by isolating the absolute value by dividing both sides by -2:
|x| = -2/(-2)
|x| = 1
Since the absolute value of a number is always non-negative, we know that |x| = 1 is equivalent to x = 1 or x = -1.
Therefore, the solutions to the equation -2|x| = 4 are x = 1 and x = -1.
To represent these solutions on a number line, we can plot the points -1 and 1, and draw a line segment connecting them. This line segment represents all values of x that satisfy the equation.
Here is one possible representation of the solutions on a number line:
```
<------|-----o-----|----->
-1 0 1
```
The open circles at -1 and 1 indicate that these points are not included in the solution set, since the absolute value of a number is always non-negative. The line segment between -1 and 1 represents all values of x that satisfy the equation -2|x| = 4.