Transformation rule: A=2,-1 B=2,-4 C=4,-2 A1=(-2,-1) B1=(-2,-4) C1=(-4,-2) A2=(-2,-1) B2=(-2,-4) C2:(-4,-2) A3=(0,-2) B3=(0,5) C3=(2,3)

Step 1 ：Draw points A, B, and C with coordinates A=(2,-1), B=(2,-4), and C=(4,-2).

Step 2 ：Draw points A1, B1, and C1 with coordinates A1=(-2,-1), B1=(-2,-4), and C1=(-4,-2).

Step 3 ：Draw points A2, B2, and C2 with coordinates A2=(-2,-1), B2=(-2,-4), and C2=(-4,-2).

Step 4 ：Draw points A3, B3, and C3 with coordinates A3=(0,-2), B3=(0,5), and C3=(2,3).

Step 5 ：The transformation rule is a rotation of 90 degrees counterclockwise about point B. So, we need to find the image of point C after the rotation.

Step 6 ：Point C is 2 units to the right and 2 units above B, so its image after the rotation will be 2 units to the left and 2 units above B.

Step 7 ：Therefore, the coordinates of the image of C after the rotation are \((2-2, -4+2)=\boxed{(0,-2)}\).