Inheritance of acquired characters would see the mice on brown soil grow more brown over time for camouflage while the mice on light colored soil would grow lighter for the same reason. This would occur over generations, but could also occur in part in a given generation--that is, those mice would become darker in a generation, pass that on to their offspring, and so forth. Evolution by natural selection would see darker mice on dark soil, or lighter mice on light soil, survive and contribute more to the next generation as natural selection led to the early deaths of mice which contrasted with the soil color. This would repeat generation after generation as mice camouflaged by the soil would be selected for.
Work Step by Step
Inheritance of acquired traits cannot happen because there is no mechanism for acquired traits to be encoded and passed on. Natural selection acts on what is already encoded in the genes, which is possible.