To rotate a point 180 degrees counterclockwise around the origin, you can use the following transformation:
\[ (x, y) \rightarrow (-x, -y) \]
Given the point (-4, -6), we apply the transformation:
\[ (-4, -6) \rightarrow (4, 6) \]
Therefore, the new point after a 180-degree counterclockwise rotation is (4, 6).