Did you rmb to balance your equation? It should be:
2HCl + MgO --> MgCl2 + H2O
So n(MgO) = 1/2 * n(HCl) used
= 1/2 * 0.19606mol
= 0.09803mol (instead of 0.19606mol which is what you got)
From there,
since n(MgO) in the 100mL aliquot = 0.09803mol,
then n(MgO) in the original 1L solution should be 0.9803 mol.
0.9803mol * (24.31+16.00)g/mol = 39.5...g
%MgO = 39.5../40.6 * 100%
= 97.3%
therefore D
Hope that helps