Blue eye colour in humans is recessive to brown eye colour. The expected children of a blue-eyed woman and a brown-eyed man who had a blue-eyed mother are likely to be:

The correct option is C Either blue-eyed or brown-eyed
The recessive character is expressed only in homozygous condition. Thus, blue-eyed woman will have 'bb' genotype, while brown-eyed man may have 'BB' or 'Bb' genotype.
Since, the man had a blue-eyed mother, he will get one recessive (blue) allele from the mother. This also suggests that he got the brown allele from the father. So, he will have 'Bb' genotype. The cross can be explained as follows:


The ratio of brown-eyed to blue-eyed offspring will be 1:1.
So, this indicates that there is an equal chance of getting a blue-eyed or brown-eyed offspring.