To 20 mL of .2 m nitric acid are added successive amounts of a base of unknown concentration. Neutrality is reached after the addition of 40 mL of the base. What was the OH of the original base solution? assume that it was 100% ionized.

Assuming you meant 0.2 M and not 0.2 m, then

HNO3 + OH^- ==> NO3^- + H2O
mols HNO3 = M x L = 0.02 x 0.2 = 0.004
mols OH- = the same since 1 mol HNO3 reacts with 1 mol OH-.
Then M OH- = mols OH-/L OH- = 0.004/0.04 = 0.1 M.
Now let's be careful here. That 0.1M is the (OH^-); it is NOT the concentration of the original base. There is no way of knowing the concentration of the original base because nothing in the problem tells you that is is MOH, M(OH)2, or M(OH)3 or whatever.