The coefficient of y is 8, which is 4p, so p=2. That is the distance the directrix is below the vertex. The directrix is below the vertex because the parabola opens upward.
The vertex can be found by completing the square.
x^2 +16x +64 = 8y -16 +64
(1/8)(x +8)^2 -6 = y +6
The vertex is (-8, -6), so the directrix is ...
y = -8
