Answer: The possible eye color of the offsprings will be brown eyes.
Explanation: When a homozygous blue eye (bb) woman crosses with a homozygous brown eye (BB) man all their offsprings will be heterozygous brown eye (Bb). The Bb genotype will manifest as brown eyes because the allele contains one gene for brown eye (B) which is dominant.
See the attached punnet square for more information.