Study Sanhedrin folio 23B with parallel Hebrew-English text, traditional commentary, and modern study tools. Free access to Babylonian Talmud online.
And Rav Dimi, son of Rav Naḥman, son of Rav Yosef, says: This is referring to a case where the litigant accepted one of these people upon himself as one of the judges, in addition to two fit judges. Since the dispute between R' Meir and the Rabbis with regard to a litigant retracting his acceptance
The Talmud answers: The statements in both mishnayot are necessary. As, had the Mishnah taught this dispute only with regard to a litigant who said: My father is trusted to adjudicate for me, or: Your father is trusted to adjudicate for me, one might have reasoned that only in this case did the Rabb
And conversely, if the Mishnah would teach us their dispute only with regard to this case, where a litigant effectively accepted one witness as equivalent to two, one might have reasoned that specifically in this case R' Meir says that he can retract his acceptance. But in that case, where he accept
The Talmud asks: But from the fact that in the former clause the Mishnah teaches that one litigant can disqualify the judge, in singular, chosen by the other litigant, and in the latter clause the wording is his witnesses, in plural, evidently the Mishnah teaches this specifically with regard to a
R' Elazar said: The Mishnah is referring to a case where the litigant and another person come to disqualify the witnesses, testifying that they are disqualified from bearing witness.