To determine the value of \( x \) for point D, which is represented as \( (x, 4) \), we can analyze the diagram features and relationships between the points A, B, and C.
Points A, B, and C are given as:
- Point A: \( (0, 12) \)
- Point B: \( (0, 4) \)
- Point C: \( (9, 0) \)
From the coordinates, we notice that points A and B lie on the y-axis, which implies:
- Point A is directly above point B since both share the same x-coordinate (0) but have different y-coordinates.
Point D is given as having a y-coordinate of 4, same as that of point B. This suggests that point D must lie at the same horizontal level as point B.
Since point D is given in the form \( (x, 4) \), it means that \( D \) has a y-coordinate of 4. To find the value of \( x \), it is essential to understand any existing relationships or distances between these points. As per general observation based on the provided coordinates, point D could likely align horizontally with point C, considering point D is seeking a position horizontally relative to points B in a manner where it completes a certain geometric configuration or relationship.
To find an explicit relationship, we recognize:
- Points A and B having \( (0, 12) \) and \( (0, 4) \) suggests some elevation between them along the y-axis.
- Meanwhile, point C's x-coordinate is 9 while D's y-coordinate aligns with B.
Assuming from geometrical arrangements and lines:
- The x-coordinate for point D \( (x, 4) \) might be \( (9, 4) \) if we are assuming horizontal alignment across line intersections.
Hence: The most reasoned point for \( D \) is to sit directly parallel to C but maintaining the same y-velocity zone as \( B \). Conclusively, the value of \( x \) at point D can be affirmed as:
\[ \boxed{9} \]