The correct spelling of the phrase "study at thoughtful" can be explained using the International Phonetic Alphabet (IPA). The word "at" is pronounced with the sound /æt/. The word "thoughtful" is pronounced with the sounds /θɔtfəl/. This means the "th" is pronounced with an unvoiced dental fricative and the "o" with a short "o" sound. The "ful" is pronounced with a schwa sound followed by an "l" sound. So, the correct spelling of the phrase is "study at thoughtful" with "thoughtful" pronounced as /θɔtfəl/.