Mike D. seems to have the correct solution, or what the answer the problem was probably intended to have.
But when you have one equation, with 2 unknowns, there're an infinite number of solutions.
For example, let x=0, then solve for y. You have -9i=-8+3yi
3yi = 8-9i, then divide by 3i
y=-3 - (8/3i) = -3 -(8i/-3)
Or let y=0, then 4x-9i=-8
4x=-8+9i, divide by 4
x = -2 +9i/4 = -2 + (9/4)i
There is no unique solution, although it's common to write a complex number as the real term plus the imaginary term. So 4x would be real and 3yi the imaginary component. Then 4x=-8, x=-2 and
But x and y could also be complex with each having a real and imaginary component. Then there are an infinite number of solutions