What kind of inheritance is it when the offspring have spots of different colors from its parents? Like a brown dog with a white dog makes a white/brown spotted dog.

In dogs, spots of brown are controlled by the S locus, the brown spots on white indicate piebald inheritance.

http://www.bordercolliesociety.com/index_breedcolor.htm

Notice that the color, the shade, the hair tinting at the base, the spotting, and markings are all controlled by different genetic loci.

The kind of inheritance you are describing is known as "codominance" or "incomplete dominance." In this case, when a brown dog and a white dog mate, their offspring show a combination of both colors, resulting in a white/brown spotted coat.

To understand how this works, we need to discuss a little bit about genetics. Dogs have genes that determine the color of their coat. These genes come in different forms or variations, called "alleles." In the case of coat color, there are multiple alleles that can produce different colors.

In codominance, two different alleles for coat color are present in the parents. Let's say the brown dog has the allele for brown color (B), and the white dog has the allele for white color (W). In codominance, both alleles are expressed and are equally dominant, meaning neither one is completely dominant over the other.

When the brown dog and the white dog mate, their offspring inherit one allele from each parent. In this case, some offspring inherit the brown allele (B) from the brown dog, while others inherit the white allele (W) from the white dog. These alleles are both expressed in the offspring, resulting in a mixture or blend of colors, commonly seen as spots.

To determine the color of each offspring, we can use a Punnett square, which is a tool used to predict the possible genetic outcomes of a cross between two individuals. Assuming Brown (B) is dominant over white (W), the Punnett square for the cross would look like this:

| B | W
--------|----------|------
B | BB | BW
W | BW | WW

From the Punnett square, we can see that there are four possible combinations of alleles in the offspring: BB (brown), BW (white/brown spotted), BW (white/brown spotted), and WW (white).

Therefore, in this case of codominance or incomplete dominance, the brown dog and white dog produce offspring with a white/brown spotted coat.