To determine the correct value of \( k \) in the equation \( y = |x - 4| + k \), we need additional information from the graph you're referring to. The value of \( k \) will shift the graph vertically.
- If \( k \) is positive, the graph shifts upwards.
- If \( k \) is negative, the graph shifts downwards.
If you could provide characteristics from the graph such as where the ball hits the wall and the point where it enters the hole, I would be able to help you find the correct value of \( k \). Without that information, I cannot definitively say which of the responses is correct (4, -4, 8, or -8). Please provide more details from the graph or the situation.