To find the area bounded by the curves y^2 = 9x and x - y^2 = 0, we need to determine the points of intersection of these two curves and then find the area between them.

1. Finding the points of intersection:
To find the points of intersection, we can set the two equations equal to each other:
9x = x - y^2
Rearranging the equation, we have:
8x = -y^2
Dividing by -1, we get:
y^2 = -8x
Since the square of a real number cannot be negative, we conclude that there are no real solutions to this equation. Therefore, the two curves do not intersect in the real plane.

2. Understanding the curves:
The equation y^2 = 9x represents a parabola that opens to the right with its vertex at the origin (0, 0). The equation x - y^2 = 0 represents a sideways parabola that opens to the left with its vertex at the origin.

3. Sketching the curves:
Since the two curves do not intersect, we can determine the area bounded by the curves by considering the area under the curve y^2 = 9x and above the x-axis. This is a part of the parabolic region.

4. Calculating the area:
To calculate the area, we integrate the equation y^2 = 9x with respect to x from x = 0 to x = a, where a is the x-coordinate of the point where the two curves would intersect if they did.
∫(0 to a) y^2 dx = ∫(0 to a) 9x dx
Using the power rule of integration, we have:
[3x^2] (0 to a) = 3a^2

5. Conclusion:
Since the two curves do not intersect, the area bounded by them is 0. Therefore, the correct answer is option B) 0.