A 4x4 grid is colored in a checkerboard pattern. How many squares are rotated to a different colored square when the grid is rotated 180 degrees about its center?

Rotational symmetry of order 2 means that a figure looks identical after a rotation of $180^\circ$ about its center. For a square grid, the center of rotation is the geometric center of the grid.

A 4x4 grid has 16 squares. The center of the grid lies at the intersection of the lines dividing the grid into four 2x2 quadrants. This means the center of rotation is not located within any single square.
If we label the squares by coordinates $(r, c)$ where $r$ is the row number (1 to 4) and $c$ is the column number (1 to 4