Answer
9.07 m from the center.
Work Step by Step
The silent points are located at angles that satisfy
$sin \theta=\frac{m \lambda}{a}$, where $m=\pm 1, \pm 2…$.
Find the first angle.
$sin \theta_1=\frac{\lambda}{a}$
$$\theta_1 = sin^{-1}(\frac{9.00cm}{12.0cm})=48.59^{\circ}$$
The distance to the first minimum from the center, point O, is $y_1=(8.00m) tan \theta_1=9.07 m$.
Note that we CANNOT use the small-angle approximation; the sine and tangent are not close to one another.
There are no real solutions for m = 2, 3, etc.
