To find the coordinates of point \( P' \) after translating point \( P \) 6 units down and 2 units to the right, we need to start with the original coordinates of point \( P \).
Given that the coordinates of \( P \) are \( (4, 6) \):
- 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 \( P' \) would be \( (6, 0) \).
The correct response is: (6, 0) \( \left( 6, 0 \right) \)