To translate the point P, which is at coordinates \( (4, 6) \), 6 units down and 2 units to the right, we can follow these steps:
-
Move 6 units down: This means we subtract 6 from the y-coordinate.
- New y-coordinate: \( 6 - 6 = 0 \)
-
Move 2 units to the right: This means we add 2 to the x-coordinate.
- New x-coordinate: \( 4 + 2 = 6 \)
So, the new coordinates of \( P' \) after the translation will be \( (6, 0) \).
Therefore, the correct answer is \( (6, 0) \).