The directrix of the parabola 12(y+3)=(x-4)2has the equation y =-6. Find the coordinates of the focus of the parabola.

A vertical line is described by the x-coordinate only.  There is no slope involved.  (the slope of a vertical line is undefined.)
For example,
The vertical line that passes through the point (5,2) is x=5, because all points x=5 passes through all points of the form (5,k), where k is any real number.