Answer
$n=14$
Work Step by Step
We can find the required number of dark fringes as follows:
$n=\frac{Wsin\theta}{\lambda}$
As $W$ and $\lambda$ are constants and $n$ is maximum if $sin\theta$ is maximum, we know that the maximum value of $sin\theta=1$
$\implies n=\frac{W}{\lambda}$
We plug in the known values to obtain:
$n=\frac{8\times 10^{-6}m}{553\times 10^{-9}m}$
$n=14$