Final answer:
The nonrecombinant progeny are the ones displaying the parental phenotypes, which are the 426 red eyes with white-banded wings and the 418 wild-type eyes with wild-type wings. The recombinant progeny are those with new combinations of traits, which are the 19 red eyes with wild-type wings and the 16 wild-type eyes with white-banded wings.
Step-by-step explanation:
In the scenario described, where silkmoths with red eyes (re) and white-banded wings (wb) are encoded by two mutant alleles that are recessive to the wild-type traits, the nonrecombinant progeny resulting from a test cross with the F1 generation are the ones that display the parental phenotypes, which in this case, are the most common phenotypes observed in the progeny. The nonrecombinant progeny are the 426 red eyes, white-banded wings and the 418 wild-type eyes, wild-type wings. On the other hand, the recombinant progeny are the ones that show new combinations of traits that were not present in the parental generation, which in this scenario are the 19 red eyes, wild-type wings and the 16 wild-type eyes, white-banded wings.