What is the equation of directrix of parabola (4x-3)^2 = -64(2y+1) ?

(4x-3)^2 = -64(2y+1) --->16(x-(3/4))^2 = -128(y+(1/2)) --->(x-(3/4))^2 = -8(y+(1/2)) ---> the equation of directrix y = (-1/2)+2=3/2

Your equation can be rewritten as
.. (x -3/4)^2 = -8(y +1/2)
This is the equation of a parabola with vertex (3/4, -1/2) and vertex-to-focus distance (p) such that
.. -8 = 4p
.. p = -2

The directrix will have equation
.. y = -1/2 -p = -1/2 -(-2)
.. y = 3/2