A black mouse mates with a brown mouse, why are no brown offspring produced

The black mouse has a dominant gene and the brown mouse has a recessive gene

Because the black mouse is homozygous.

The black color in mouses is dominant, and the brown is recessive. When a parent is homozygous, their children need to have their gene. Because in this case the trait is black, it dominates brown in all children.

The table is BB*bb = Bb, Bb, Bb, Bb = 100% heterozygous genotype = 100% black phenotype.