We say an allele g is recessive relative to an allele G when the phenotype characterized by g is only present in individuals with the combination gg. That is, g will not manifest if combined with G, due to G's dominance over g.
With that in mind, we know that the offspring of goats in our case needs to be made up completely of homozygote individuals of the type gg. Here g denotes the allele responsible for causing goats to faint.
If any of the goats parents possess the allele G (GGxGG, GgxGg or ggxGg), then there is a chance that this allele will pass down to at least one goat of the offspring. But we don't want this to happen. From that, we can deduce that neither of them can have the allele G, and thus, both of them must be homozygous recessive gg for their offspring to be 100% fainting goats! Or, talking about the phenotypes, both parents must also be fainting goats.