Well, considering it is autosomal recessive, the possible genotypes of the parents of IV 2 must be heterozygous (let's say Aa). Now, we cross them and get AA, Aa, Aa, aa as all possible genotypes of their offspring.
Tay Sachs disease is autosomal recessive as deduced by the pedigree. Affected individuals must be homozygous recessive (aa). Unaffected individuals may be homozygous dominant or heterozygous. So therefore we can rule out the possibility of unaffected individuals (like Mr IV 2) being homozygous recessive (obvious). So now we are left with Aa, Aa and aa. There is a 2/3 chance it is heterozygous for Tay Sachs disease.
Basically, although technically there is a 1/2 chance he's heterozygous, because we know he is unaffected by an autosomal recessive disease, we can narrow down our possibilities to 2/3.
Lol my fail explanation sorry