To have a child with blonde hair (bb), a parent must contribute a recessive allele (b). Since the parent with brown hair (Bb) contributed one recessive allele (b) to the child, the other parent must also have contributed a recessive allele (b) to make the child's genotype bb.
Therefore, the other parent must have at least one recessive allele (b) in their genotype. This means the possible combinations for the other parent can be either Bb (brown hair) or bb (blonde hair). However, since having blonde hair is specified as recessive, the other parent could be Bb (brown hair) or bb (blonde hair).
Given the choices, the correct response is:
Bb, brown hair