There are two ways to do this, the long way (which I prefer) and the short way (which most other people prefer).
The long way first:
2W + 3X ==> 3Y + Z
We are given 5W and 6X. Take these one at a time.
Use the coefficients in the balanced equation to convert units of W to units of either product. Let's choose Z.
5W x (1 unit Z/2 units W) = 5x(1/2) = 2.5 units Z.
Next we convert X.
6X x (1 unit Z/3 units X) = 6 x (1/2) = 2 units Z.
Both answers can't be right; the correct one is ALWAYS the smaller value and the reagent producing that value is the limiting reagent. Therefore, X is the limiting reagent and 2 units of Z will be formed.
Second method (and shorter):
Take EITHER W or X and convert to the other one. I'll do both so you can see how it works.
5W x (3 units X/2 units W = 5 x (3/2) = 15/2 = 7.5 units X; i.e., 5 units of W would require 7.5 units of X. Do we have that much? No, we have only 6; therefore, X must the limiting reagent.
Just to make sure we didn't goof, convert 6 units X to units of W.
6X x (2 units W/3 units X) = 6 x (2/3 = 4 units W. Do we have that much? Yes, therefore, the OTHER one (X) must the limiting reagent.
This may be more than you ever wanted t know about limiting reagent work BUT it's complete. Use either method you feel comfortable with.