What is the rule for a 180 degree counterclockwise rotation?

First of all, if the rotation is 180 degrees then there is no difference clockwise and anti-clockwise so the inclusion of clockwise in the question is redundant.

In terms of the coordinate plane, the signs of all coordinates are switched: from + to - and from - to +.

So

(2, 3) becomes (-2, -3),

(-2, 3) becomes (2, -3),

(2, -3) becomes (-2, 3) and

(-2, -3) becomes (2, 3).