Oh I see what you're all saying now. I agree, 1/16 looks right.
Edit: Nope, nevermind.. back to 1/64, here's why.
Generation III is 100% carrier (both maternal and paternal sides).
For some reason the tendency to assume heterozygosity resonates with me. I remember my genetics teacher explained this, but I don't remember why or how.
So, assuming all 4 maternal grandparents are heterozygotes, you now have (1/2)*(1/2) for BOTH maternal and paternal odds and another (1/2)*(1/2) for baby
Thus, (1/2)^6.
You get (1/2)^4 if you assume that 2 grandparents are homozygous dominant and the other 2 are heterozygotes though.