Final answer:
The correct scientific name of an organism with the genus Felis and the species domesticus is Felis domesticus, following the rules of binomial nomenclature.
Step-by-step explanation:
If an organism has the genus Felis and the species domesticus, the correct scientific name of the organism following the binomial nomenclature system would be Felis domesticus. This naming convention was developed by Carolus Linnaeus and involves using a two-part Latin name, where the genus name is capitalized while the species name is in lowercase, and both should be italicized. Therefore, the correct answer is option 4) Felis domesticus.