Dilution problems are very simple: the moles of solute are constant when you add water or take out water (condensing). Given cases 1 and 2: 1 is known and 2 has an unknown that you are looking for:
n1 = n2 and M1V1 = M2V2 (concentration of solute x volume of solution = moles of solute)
In this case, we want V2, the unknown volume of the concentrated solution (note that this is a dilution problem in reverse - it doesn't matter what direction the process goes)
V2 = V1(M1/M2) (Note that the units do not need to be mole/liter and liters for these problems, any volume units will work as long as V2 and V1 are the same units and M1 and M2 are the same units.)
Another way to think through problems (multiple choice problems especially) is to realize that M and V are inverse. So whatever is done to M, the inverse is done to V going in the same direction. Here we are looking at going from .25 to 6 Molar: a factor of 24. So, the original volume of 6 M must be 25 ml*(1/24).
Please consider a tutor. Take care.
