The spelling of the word "badger skunk" can be explained using the International Phonetic Alphabet (IPA). The first syllable, "badger," is pronounced /ˈbædʒər/ with a short "a" sound followed by a "j" sound as in "jump." The second syllable, "skunk," is pronounced /skʌŋk/ with a "sk" sound as in "sky" and a "u" sound as in "bus" followed by a "ng" sound. Therefore, the correct spelling of this word is "badger skunk."