Explanation

(d)
The centres of given circles are $C_{1}( - 3,\ - 3)$ and $C_{2}(6,\ 6)$respectively and radii are $r_{1} = \sqrt{9 + 9 + 0} = 3\sqrt{2}$ and $r_{2} = \sqrt{36 + 36 + 0} = 6\sqrt{2}$ respectively
Now, $C_{1}C_{2} = \sqrt{(6 + 3)^{2} + (6 + 3)^{2}} = 9\sqrt{2}$
and $r_{1} + r_{2} = 3\sqrt{2} + 6\sqrt{2} = 9\sqrt{2}$
$\Rightarrow \ \ \ \ C_{1}C_{2} = r_{1} + r_{2}$
$\therefore$ Both circles touch each other externally