Solving a Pedigree Between Heterozygous Half-Cousins
From what I can tell, you are not including the probability of the grandfather being a carrier (it could be the grandmother who is the carrier). Calculation should go like:

P(Child is born with disorder) = P(II-2 is carrier) * P(I-2 is carrier) * P(II-3 is carrier) * P(III-2 is carrier) * P(Child is homozygous recessive)

P(Child is born with disorder) = (1/2) * (1/2) * (1/2) * (1/2) * (1/4)

P(Child is born with disorder) = 1/64