The probability of a child having blue eyes from this particular parent combination would be 0 percent, since the man has the genotype bb, which means that he can only pass the b allele to his children. The woman is homozygous for brown eyes (BB), which means that she can only pass the B allele to her children.
Therefore, all of the children of this couple will be heterozygous for eye color (Bb) and have brown eyes. To summarize, the answer is D, 0 percent probability.