To solve this translation problem:

1. Initial coordinate: The preimage coordinate is given as $(9, 6)$.
2. Translation:
   • Moving 6 units to the right: Add 6 to the x-coordinate.
   • Moving 5 units down: Subtract 5 from the y-coordinate.

Step-by-step solution:

• $x \text{-value} = 9 + 6 = 15$
• $y \text{-value} = 6 - 5 = 1$

Therefore, after the translation, the new coordinate (image) is $(15, 1)$.

The x-value of the image is $\boxed{15}$.

Do you need more details or have any questions?

Here are 5 related questions to deepen your understanding:

1. What would be the y-value of the image after this translation?
2. How do you perform a translation if you are given a vector?
3. If the original coordinate was $(9, 6)$ and the translation was 3 units left and 4 units up, what would the new coordinates be?
4. What is the general formula for translating a point $(x, y)$ by $(a, b)$?
5. What would happen if you translated the point $(9, 6)$ by $(0, 0)$?

Tip: When translating points on a coordinate plane, moving "right" increases the x-value and moving "left" decreases it, while moving "up" increases the y-value and moving "down" decreases it.