The work to get this answer is as follows:

To get a general step-by-step way to solve these then just go here.

1. First, take care of the numbers to see if they can be simplified at all. In this case the number in the numerator is 18 while the number in the denominator is 3. These numbers can be simplified.
2. Second, after you take care of the numbers, what you have left is what I consider to be the constant part of the resultant because it does not involve variables and can just be multiplied to the variable part for the final resultant.
3. Next, it is time to handle the variable part.
   1. Notice that the N and M variables are both unique, only appearing once each. While the X and Y variables appear in both the numerator and denominator.
   2. That means that we already have some of the variable part of the answer; (N^8)/(M^2). Next step is to take care of the other variables.
   3. Let's take care of the X variable first, it doesn't matter which one you take care of first. On the top we have X^3 while we have X^5 on the bottom. Now to do division of the two powers you would normally subtract the bottom variable's exponent from the top variable's exponent. The result of that would be on the top of the fraction. But what if we were to switch that, and instead subtract the top variable's exponent from the bottom variable's exponent? The result should then go to the denominator, which it would. This means that in this case, where the exponent of the variable in the denominator is bigger than the exponent of the variable in the numerator, it would work out better if we were to subtract the exponent of the variable in the numerator from the exponent of the variable in the denominator. The result would then be X^2, but now it belongs in the denominator.
   4. The next variable to take care of is the Y variable. Y^6 is in the numerator while Y(when there is no exponent shown it is implied that it is being raised to the first power). Since the exponent of the variable in the numerator is bigger, it is easier to do the subtraction the standard way which would yield Y^5. This Y^5 would be on the top of the fraction.
   5. Now you must combine the different variables. The variables belonging in the numerator are the Y and N variables. Each variable with their exponents were Y^5 and N^8. Combine these two (Y^5N^8) to get the numerator of the variable part of the result. The variables belonging in the denominator are X(X^2) and M(M^2). Combining these two form (X^2M^2) which is the denominator of the variable part of the result. Now to comibne the numerator and the denominator parts. The result would be (Y^5N^8)/(X^2M^2). This is the variable part of the solution.
4. Now with both the constant part (6) and the variable part (Y^5N^8)/(X^2M^2) of the solution all we have to do is combine them. It is quite simple, all you have to do is multiply them together. The resultant would be (6Y^5N^8)/(X^2M^2). This is the simplified form, as I have shown.