To rotate a point \((x, y)\) counterclockwise about the origin by 180 degrees, you can use the following transformation:
\[ (x, y) \rightarrow (-x, -y) \]
For the point \((-6, 4)\), we apply this transformation:
\[ (-6, 4) \rightarrow (6, -4) \]
Therefore, after rotating the point \((-6, 4)\) counterclockwise about the origin by 180 degrees, the new point is \((6, -4)\).