your told that the displacement $x$ is given by
$x= 3 \cos(4t + \dfrac{\pi}{2})$
and you need to find when $x=0$ so just set this expression equal to zero and solve it.
$0= 3 \cos(4t + \dfrac{\pi}{2})$
$0=\cos(4t + \dfrac{\pi}{2})$
Now you have to know that $\cos(\theta)=0$ when $\theta=\pi (n+\dfrac{1}{2})$ for n being some integer. Set n=0,1,2 to find the first 3 times $x=0$
so for example with n=0
$4t + \dfrac{\pi}{2} = \dfrac{\pi}{2}$
$4t=0$
$t=0$
you can solve for the t's corresponding to n=1 and n=2