The question does not state which gene is dominant, so I do not know if B is black or b is black. That does not matter though based on the parental genotypes that the question uses. I will assume that BB and Bb are phenotypically black, and bb is phenotypically white.
The initial cross is between a black (Bb) mouse and a white (bb) mouse.
The genes will sort independently, so the black individual can donate B or b. The white individual can only donate b.
Two potential offspring will be genotypically Bb. Two potential offspring will be bb. 50% show the dominant trait, and 50% show the recessive trait. That is why it does not matter if black is dominant or recessive. Half of the F1 generation could be black, and half could be white.