You may perform the division using either long division or synthetic division. Any preference?
I used synthetic div. with -2 as the divisor:
________________
-2 / 3 4 -10 0 15
-6 4 12 -24
-------------------------
3 -2 -6 12 -9
In factored form, with remainder, we then have:
(x+2)(3x^3 - 2x^2 - 6x + 12) remainder -9
If you need clarification of any part of this solution, let me know.