The correct spelling of the phrase "casts hook" follows the clear rules of pronunciation in English. "Casts" is spelled with a silent "t" as the sound is pronounced as "kasts." "Hook" is spelled as it sounds with the "h" as an aspirated consonant and the "oo" pronounced as "ʊ." The IPA phonetic transcription for "casts hook" is /kæsts hʊk/, reflecting the correct pronunciation of the phrase. The spelling of this word adheres to the standard English language pronunciation rules.