To rotate a point \(180\) degrees counterclockwise around the origin, you can use the rule that states:
\[ (x, y) \rightarrow (-x, -y) \]
Starting with the point \((-4, -6)\):
\[ (-4, -6) \rightarrow (4, 6) \]
So the new point after rotating \((-4, -6)\) by \(180\) degrees counterclockwise is \((4, 6)\).
The correct answer from the options given is:
\((4, 6)\)