There are several synonyms for the phrase "puts in other words." One could use the term "in other terms," which means to explain something using different language or terminology. Alternatively, one could use "in simpler terms" or "to rephrase," which means to express something in a clearer or more understandable manner. Another synonym is "to elucidate," which means to make something clearer or more comprehensible through explanation or elaboration. "To paraphrase" could also be used, which means to restate something using different words while retaining its original meaning. Overall, using synonyms for "puts in other words" can help to diversify one's writing and improve clarity and understanding for the reader.