To find the perimeter of a polygon, we need to add up the lengths of all the sides.
Given the vertices (-2,4), (0,4), (-2,2), (0,-2), (2,-2), and (2,0), we can determine the lengths of the sides by calculating the distance between each pair of consecutive vertices.
Let's calculate the lengths of the sides:
1. Length of the side connecting (-2,4) and (0,4) is 2 units.
2. Length of the side connecting (0,4) and (-2,2) is 2 units.
3. Length of the side connecting (-2,2) and (0,-2) is 4 units.
4. Length of the side connecting (0,-2) and (2,-2) is 2 units.
5. Length of the side connecting (2,-2) and (2,0) is 2 units.
6. Length of the side connecting (2,0) and (-2,4) is 8 units.
Now, we add up the lengths of all the sides:
2 + 2 + 4 + 2 + 2 + 8 = 20 units.
Therefore, the perimeter of the polygon with the given vertices is 20 units.