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