Answer
$y=-\frac{1}{12}x^{2} $
Work Step by Step
The distance from focus to Directix is $2\left| p\right|$
$$\Rightarrow 2\left| p\right| =6\Rightarrow \left| p\right| =3$$
If focus is on the negative $y$ axis then
$p=\left( 0,-3\right) $
$x^{2}=4py=4\times (-3)\times y=-12y\Rightarrow y=-\frac{1}{12}x^{2} $
