You can rewrite the equation into the form
.. y = 1/(4p)*(x -h)^2 +k
In this form, (h, k) is the vertex and p is the distance from the focus to the vertex, or the vertex to the directrix.
.. x^2 +4x -6 = -4y . . . . . . . . . . . add -2-4y
.. (x +2)^2 -10 = -4y . . . . . . . . . . complete the square
.. (-1/4)*(x +2)^2 +2.5 = y . . . . . . the desired form
Then the distance from vertex (-2, 2.5) to the directrix is -1, which means the directrix is 1 unit above the vertex.
The equation of the directrix is y = 3.5.
