The phrase "six of half a dozen the other" means that there are two choices that ultimately lead to the same result. Synonyms for this phrase include "six one way, half a dozen the other," "same difference," "no difference," "equivalent," "parallel," "indistinguishable," "interchangeable," and "virtually identical." These phrases are often used when a person is faced with two options and wonders if one is truly better than the other. By using such synonyms, one can convey that there is no significant difference between the options that are being considered, and that either of them would result in similar outcomes.