How to solve:

4d^4w^3*6dw^4/3d^3w*8dw^2

What you have is

4 d^4 w^3 * 6 d w^4
----------------------------
3 d^3 w * 8 d w^2

collecting powers of each variable, that is

24 d^5 w^7
-----------------
24 d^4 w^3

I think you can see what cancels out now, right?