The correct spelling for the phrase "am of family" can be explained using IPA phonetic transcription, which is a system of symbols that represent individual sounds in words. The first word, "am," is pronounced /æm/, with the vowel sound /æ/ as in "cat" and the consonant sound /m/ as in "mom." The second word, "of," is pronounced /ʌv/, with the vowel sound /ʌ/ as in "cup" and the consonant sound /v/ as in "voice." The final word, "family," is pronounced /ˈfæməli/, with the stressed vowel sound /æ/ as in "cat" and the consonant sounds /f/, /m/, and /li/.