Hi Asra,
Typically the x axis represents the independent variable, and y axis represents the dependent variable. Box and whisker plots generally use a categorical x axis, not a quantitative one. The y axis must be quantitative since you are going to display a median/mean with ranges.
I would think it makes the most sense to have your two different purification methods as your categories/independent variable. For each of your dependent variables, you can do a separate box&whisker, since the y axis for each will be different. I'd consider whether volume is really an important dependent variable for you to display. Would it make more sense to compare how much DNA total you got from each method, by calculating the mass (concentration x volume)?
Also, make sure you have a big enough sample size for the box and whisker plots to be meaningful - they would be an appropriate graph type if you have done multiple purifications using each method.
