Step 1:

The centre is at $C(4,-2)$ and one focus is $F(4,2)$.Let $F'(x_1,y_1)$ be the other focus.

Now $C$ is the midpoint of $FF'$.

Step 2:

Therefore $\large\frac{4+x_1}{2}$$=4$

$\large\frac{2+y_1}{2}$$=-2$

(i.e)$x_1=4,y_1=-6$

The other focus is $(4,-6)$