To rotate a point \((x, y)\) 90 degrees counterclockwise around the origin, you can use the transformation:
\[ (x', y') = (-y, x) \]
For the point \((-4, -6)\), we can plug in the values:
\[ x' = -(-6) = 6 \] \[ y' = -4 \]
Thus, the new point after rotating \((-4, -6)\) 90 degrees counterclockwise is \((6, -4)\).
So, the correct answer is:
\((6, -4)\)