Rashi, Rashbam and Targum Yonasan: It is after the episode of the Golden calf ¹ . Levi did not go astray then, and that is why Hashem chose them, as the Pasuk goes on to explain. It is mentioned here, following the episode of B'nei Ya'akan, because there too, the tribe of Levi did not go astray.

Ramban: It refers to the same time as "ba'Eis ha'Hi" in Pasuk 1 - after Hashem instructed Moshe to carve out a second pair of Luchos, when He made up with K'lal Yisrael and commanded them to build the Mishkan, that is when the Levi'im were chosen. ²

Seforno: It is following the sin of the Golden Calf. Moshe was pointing out that Hashem chose the Tribe of Levi to serve Him and the rest of Yisrael remained unworthy of doing so. It is a sign that he only achieved with his Tefilah that Hashem did not destroy them, but not a complete pardon.

Oznayim la'Torah: It refers to the current episode - Refer to 10:6:1:1 - where, for the tgird time, the tribe of Levi demonstrated their loyalty towards Hashem - 1. In Egypt. 2. By the Eigel, and 3. here, when they chased after the rebels who were on their way back to Egypt to return them to the camp. And since they attained a Chazakah in loyalty, Hashem designted them a special triple role - permanently for all time: 1. to carry the Aron of Hashem; 2. to stand before Hashem to serve Him and 3. to bless the people. ³

Ramban #1 (according to Rashi - Refer to 10:8:1:1): It refers to the time that Hashem designated them, or to the Mesirus Nefesh that they displayed that earned their designation. ¹

Ramban #2: Refer to 10:8:1:2.

Rashbam: Refer to 10:8:1:1 ² .

Horayos, 13a: It means that a ben Levi should be given precedence over a Yisrael ¹ - and by the same token, that the more holy always takes precedence over what is less holy.

Rashi (in Zevachim, 27a: To teach us that every 'Sheirus' must be performed inside the Azarah - and that consequently, receiving the blood must be performed in a K'li Shareis in the Azarah.

Zevachim, 16a: To confine the Mitzvah of standing whilst performing the Avodah to the Beis-Hamikdash, to preclude when serving on a Bamah. ¹

Rashi (in Eruvin, 18b): It means with the explicit (four-letter) Name of Hashem. ¹

Rashi: This Pasuk is talking about the entire Tribe of Levi, including the Kohanim. ¹

Rashi: It means to bless the people with the Name of Hashem - the way it is written. ¹

Ramban: With reference to the designation of Aharon and his descendents as Kohanim ¹ - which was a permanent appointment. ²

Refer to Bamidbar 6:23:151:1.