Answer
$y^2=12x$
Work Step by Step
We are told that the directrix is right of the origin; thus, $ p$ is the negative of the distance between the two points.
$6^2=(4)(p)(3)$
So, $p=\dfrac{36}{12}=3$
Since the vertex and focus have the same y-coordinate, the parabola must have a horizontal axis.
Now, we will write the equation for a parabola that has a vertical axis using the vertex and $p$.
$y^2=4px \implies y^2=(4)(3) \times x $
$\implies y^2=12x$
