The parametric equation of the parabola $\rm ( y - k)^2 = 2 ( x - h)$ is $\rm (x,y) = (h + at^2, k + 2at)$.

We compare the given equation of the parabola $\rm (y - 2)^2 = 2 (x + 3)$ with $\rm ( y - k)^2 = 2 ( x -h)$, we get,

$\rm (h,k) = (-3, 2)$ and $\rm a = \frac{2}{4} = \frac{1}{2}$

Now, we solve for the value of x,

$\rm x = h + at^2$

$\rm or, x = -3 + \frac{1}{2} t^2$

And, we solve for the value of y,

$\rm y = k + 2at$

$\rm or, y = 2 + 2 \cdot \frac{1}{2} \cdot t$

$\rm \therefore y = 2 + t$

Hence, the required parametric equation of the parabola $\rm ( y - 2)^2 = 2 (x  + 3)$ is $\rm x = -3 + \frac{1}{2} t^2$ and $\rm y = 2 + t$.