To solve this equation, we can first try to factorize it.

x^3 - 6x^2 - 4x + 24 = 0

Group the terms:

x^2(x - 6) - 4(x - 6) = 0

Factor out (x - 6):

(x^2 - 4)(x - 6) = 0

Factor further using the difference of squares:

(x + 2)(x - 2)(x - 6) = 0

Now, set each factor to zero and solve for x:

x + 2 = 0
x = -2

x - 2 = 0
x = 2

x - 6 = 0
x = 6

Therefore, the solutions to the equation x^3 - 6x^2 - 4x + 24 = 0 are x = -2, x = 2, and x = 6.