Answer
$${\left( {y - 2} \right)^2} = 12x$$
Work Step by Step
$$\eqalign{
& {\text{parabola with focus at }}\left( {3,2} \right){\text{ and directrix }}x = - 3 \cr
& {\text{The directrix is }}x = - p + h,{\text{ then }} \cr
& {\text{the equation of the parabola is of the form }}{\left( {y - k} \right)^2} = 4p\left( {x - h} \right) \cr
& \cr
& {\text{Focus }}\left( {p + h,k} \right):\left( {3,2} \right),\,\,\,\,\,\,p + h = 3,\,\,\,\,\,k = 2 \cr
& x = - p + h,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, - p + h = - 3 \cr
& {\text{Solving these equations we obtain:}} \cr
& p = 3{\text{ and }}h = 0 \cr
& \cr
& {\text{The equation of the parabola is}} \cr
& {\left( {y - 2} \right)^2} = 4\left( 3 \right)\left( {x - 0} \right) \cr
& {\left( {y - 2} \right)^2} = 12x \cr} $$
