What is the molarity of the original barium hydroxide solution?

find moles:
0.0454 L of 0.910 mol/Litre HCl = 0.041314 moles HCl
0.0241 L of 1.31 mol/Litre NaOH= 0.031571 moles NaOH

 the HCl was finally neutralized by the NaOH,
find how many moles of HCl had arleady been neutralized by the Ba(OH)2:
 0.041314 moles HCl -  0.031571 moles NaOH  = 0.009743  moles of HCl was previously neutralized


by the equation:
2 HCl  &  1 Ba(OH)2  BaCl2  &  2 H2O
0.009743  moles of HCl reacts with 1/2 as many moles of Ba(OH)2 ; 0.0048715 moles Ba(OH)2

find the molarity of that 38.1 ml Ba(OH)2 solution:
0.0048715 moles Ba(OH)2   /  0.0381 litres = 0.12786 Molar


your answer, rounded to 3 sig figs is
0.128 Molar Ba(OH)2