The moles of OH- ions from the Ba(OH)2 must equal the moles of H+ ions from the HNO3 in order for them to neutralize. You must multiply volume (in liters) by the molar to get number of moles. There is 0.90 molar of OH- because there is twice as many OH- as there is Ba(OH)2. The molarity of H+ is unknown.
Let X be the unknown molarity
(0.0182 L)(0.90 M) = (0.0385 L)(X M)
X = 0.43 M (2 significant figures)
So the molarity of H+ ions, and therefore HNO3 is 0.43 M
In a chemical reaction, reactants that are not used up when the reaction is finished are called excess reagents. The reagent that is completely used up or reacted is called the limiting reagent, because its quantity limits the amount of products formed.