The equation of the sphere is $x^2+y^2+z^2-6 x-12 y-2 z+20=0$


So, the centre of the sphere is
$(-u,-v,-w)=(3,6,1)$
given the one end of the diameter is $(2,3,-3)$, let the other end of the diameter is $(\alpha, \beta, \gamma)$. Since, $O$ is the mid point of the diameter, then
$(3,6,1)=\left[\frac{\alpha+2}{2}, \frac{\beta+3}{2}, \frac{\gamma-3}{2}\right]$
$\Rightarrow \quad \frac{\alpha+2}{2}=3, \alpha=4$
$\Rightarrow \quad \frac{\beta+3}{2}=6, \beta=9$
$\Rightarrow \quad \frac{\gamma-3}{2}=1, \gamma=5$
Hence, the other end is $(4,9,5)$.