The correct spelling of the phrase "outing the way" is /ˈaʊtɪŋ ði ˈweɪ/. The first word, "outing," is spelled with "ou" to represent the diphthong /aʊ/ sound. The second word, "the," is spelled with the voiceless dental fricative sound /ð/. The final word, "way," is spelled with the long "a" sound /eɪ/. Overall, this phrase is spelled phonetically to accurately represent its pronunciation.