They'll most likely cacth the skin fungus too. the towel may wipe off bacteria of the fungus and dead skin cells, and the other person using it may be wiping those bacteria and dead skin cells on them too.
Polygenic inheritance is simply a form of inheritance whereby the trait of the individual or the animal is gotten from the cumulative effects of several genes. In such case, there are many genes which control the expression of the trait. This is quite different from the monogenic inheritance whereby the trait is as a result of the expression of just only one gene.
Since Pietro has two dogs that are related, and one of the dogs has tan fur and the other has brown fur, then this means there's more than one gene which is expressed in this case.
In conclusion, the answer to the question is polygenic inheritance.
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It looks correct to me. Good job