The problem asks to reflect the point $(6, -6)$ across the line $x = 0$ and determine the new $x$-value.

Reflection across the line $x = 0$:

• When reflecting a point across the line $x = 0$ (the y-axis), the $x$-coordinate changes its sign, while the $y$-coordinate remains the same.

Thus:

• The original point is $(6, -6)$.
• After reflection, the new point is $(-6, -6)$.

Final Answer:

The $x$-value after the reflection is $\mathbf{-6}$.

Would you like more details or have any questions?

Here are 5 related questions you can consider:

1. What happens when reflecting a point across the y-axis versus the x-axis?
2. How does the reflection change for points on the y-axis itself?
3. Can you describe the effect of reflecting a point across the origin?
4. What is the general rule for reflecting points over any vertical line $x = a$?
5. How does the distance from the reflection line influence the new point's location?

Tip: When reflecting across vertical or horizontal lines, only the coordinate corresponding to that axis changes sign. The other coordinate remains unaffected!