Let H=horizontal striping and h=vertical striping. The striping seen in the image shows clear codominance: both phenotypes are equally well visible in the child. The father must be HH and the mother must be hh since this codominance means only homozygotes would show only horizontal or only vertical striping. The child would be an Hh heterozygote.
Work Step by Step
The key here is to see that the "phenotype" is mixed, with neither state masked even in part in the child. That leads to a diagnosis of co-dominance, making the deciphering of all three genotypes straightforward.