Since 2i is a root of f(x) and f(x) has real coefficients, , -2i is also a root.
Since f(x) has degree 3, there can't be more than 3 roots.
The roots are 2i, -2i, and -4
f(x) = a(x-2i)[x-(-2i)](x-(-4)]
Since f(-1) = -45, 15a = -45
So a = -3
f(x) = -3(x3+4x2+4x+16) = -3x3-12x2-12x-48