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.