In the beginning of the Parsha, Yitro arrives with Tzipporah, Eliezer, and Gershom, and a whole family reunion takes place. Everyone is happy to see each other and there is a big feast with korbanot to Hashem. Then, in Pasuk 13, the Torah records “Vayehi Mimacharat” “And it was on next day.” There is a famous question asked on this, which day is this is next day after?
Taking the simple Pshat of the Pasuk, the Ibn Ezra says that it must be the day after the arrival of Yitro. However, Rashi, quoting the Midrash, says that it refers to the day after Yom Kippur. Rav Yosef Dov Soloveitchik HaLevi explains the phrase as meaning that when Moshe first sat in judgment, it was “the day after” the first judgment. Moshe had to learn how to judge, so he learned different Halachot such as Pshara, compromise based on what Hashem did on Yom Kippur. It only makes sense that the day after Moshe saw Hashem judge Bnei Yisrael, he, Moshe, learned the manner in which to judge others.
Additionally much support can be given to both Rashi and the Ibn Ezra. First, in support of the Ibn Ezra, it is very logical that it was the day after Yitro’s arrival because it flows with the order in the Pasuk. However, in support of Rashi, one may say there is an indication in Pasuk 12 that it was a day after Yom Kippur because the Torah mentions that people ad bread and a feast, as if it was food before the fast. Additionally, it is possible to say that this is a source in the Torah to have a Seudat Mafseket before Yom Kippur, as they had some food before Yom Kippur.