|Image is from Wikimeida Commons and is copyright free.|
The striking dog on the right is an Australian shepherd. Wikimedia Commons lists this dogs as a "red merle," which is...well, wrong. Red merle in the Aussie breed is actually merled liver, and this dog is not merled liver. It is merled sable, which is clearly seen in the black hairs at the dog's ears and tail. A liver dog will never have black hairs (or pigment, and this dog has a black nose).
Technically, you can call a sable merle "red merle," since sable is often called red, especially if the black overlay is very minimal. However, like in several breeds, all liver Aussies are called "red" and the few sable Aussies that show up are called just that: sable. Virtually all cases where merle and liver occur together in the same breed involves the merled liver dogs being called "red merle," which is really a terminology issue. You can read more about my issues with canine color terminology in Some Notes on Terminology.
Anyway, as I said this dog is sable. Due to the prevalence of tan point in the breed and the relative rarity of sable, the most likely genotype for this dog is Ayat sable carrying tan point.
Though this dog has black pigment, it is very likely that it carries liver since liver is also quite common in Australian shepherds. As such, I suspect this dog is Bb non-liver carrying liver.
This dog is also merle. It's actually quite unusual for the red parts of a dog's coat to be affected by merle, but in this is clearly one of the cases where it is. You can also see gray spots on the head and ears, most notably on the dog's right ear, and a pink spot on its nose. These are other signs that the dog is merle. I highly doubt this dog is homozygous merle, and as such it has to be Mm merle.
The white on the dog is controlled by one final gene, the white spotting gene. This dog has Irish white, which is the most common form of white seen in the breed. Though it can't really be determined, it is quite possible this dog is actually collared Irish. The coverage of Irish white varies greatly and is most likely controlled by unknown plus and minus modifiers. Either way, it is sisi Irish white.
So, that is Ayat Bb Mm sisi or sable merle and white (carrying liver and tan point).
As for the second dog that is happily rolling around in the wood chips, it is a Labrador retriever in the breed's most common color of black. Here are my thoughts on its genotype:
Chocolate in Labradors is caused by the liver gene, and as such this dog is either BB or Bb. But which? I suspect this dog is a non-carrier as there are fewer chocolates than blacks or yellows. As such, it would be BB non-liver.
Yellow in Labradors is caused by the recessive red, which means this dog must be either EE, EEm, Ee, EmEm, or Eme. Black masking does occasionally appear in mismark Labs with tan points. However, it is comparatively unusual. Yellow is the second most common Labrador color, and as such I suspect this dog is Ee non-recessive red carrying recessive red.
All Labradors except for very few exceptions (i.e. mismarks like tan or brindle pointing) are dominant black. No, I'm not joking. The chocolate (liver) and yellow (recessive red) colors are genes that either dilute the black (liver) or cover the black (recessive red). Under both, the dog is in fact black. This means that this dog must be KK black.
As for the white on the dog, I suspect that it is residual white, a common phenomenon in dogs when a genetically solid colored dog has a small amount of white at the chest, toes, or both. That would make this dog SS solid with residual white.
So, that is BB Ee KK SS or black with residual white (carrying recessive red).