Answer:
The correct option is C.
Step-by-step explanation:
From the given figure it is clear that the vertices of the parallelogram are (0,0), (0,-6), (4,-8) and (4,-2).
If a figure rotated 180° about (a,b), then

If the figure rotated 180° about (2,-4), then


So, the vertices of image after rotated 180° about (2,-4) are




The vertices of image are same as vertices of preimage. So, 180° rotation about (2,-4) maps the figure onto itself.
Therefore the correct option is C.