To translate the point \( P(4, 6) \) 6 units down and 2 units to the right, you will adjust the coordinates as follows:
- Move 6 units down: This means you will subtract 6 from the y-coordinate.
- Move 2 units to the right: This means you will add 2 to the x-coordinate.
Starting with the original coordinates of \( P(4, 6) \):
- New x-coordinate: \( 4 + 2 = 6 \)
- New y-coordinate: \( 6 - 6 = 0 \)
Thus, the coordinates of \( P' \) after the translation are \( (6, 0) \).