To rotate a point \((x, y)\) by 180 degrees counterclockwise around the origin, you can use the formula:
\[ (x', y') = (-x, -y) \]
For the point \((-4, -6)\), we can apply this formula:
\[ x' = -(-4) = 4 \] \[ y' = -(-6) = 6 \]
Thus, the new point after a 180-degree counterclockwise rotation is:
\[ (4, 6) \]