To rotate a point \( (x, y) \) by 180 degrees counterclockwise around the origin, you can use the formula:
\[ (x, y) \rightarrow (-x, -y) \]
For the point \( (-4, 6) \):
- Apply the transformation: \[ (-4, 6) \rightarrow (4, -6) \]
Thus, the point \( (-4, 6) \) rotated 180 degrees counterclockwise around the origin is \( (4, -6) \).