Each one's color. Thus the meaning of “their fathers’ houses” was the names of their fathers that were engraved on the breastplate. But since this is a forced explanation in the understanding of “their fathers’ houses,” Rashi gives another explanation. Nonetheless, according to the other explanation one may question the connection between the word “banner” and “the insignia of their fathers’ houses,” therefore he also needs the first explanation.

When they carried him. Meaning that accordingly one must say that “banner” is a term of gathering as in “ודגלו עלי (and encamped around me)” (Shir HaShirim 2:4). This teaches that each banner was with its group.

At the distance of a mil. One might ask: Previously in Parshas Yisro (Shemos 19:2), Rashi explained that נגד ההר (opposite the mountain) meant to its east, because any time that you find the word נגד it implies facing east, even if it comes as a construct (opposite something). The answer is: Here it is written “around the Tent of Meeting they shall encamp” so it is not possible that they were all facing east. Thus Rashi explains that it is a term of distance. Furthermore, I have found that one may learn this through a gezeirah shavah (comparison); the Torah here says מנגד (opposite) and elsewhere it says ותשב מנגד הרחק (“and sat facing him about the distance”) (Bereishis 21:16). Thus, just as there it refers to distance, so too here it refers to the distance. A mil is a distance of two thousand amos [the maximum distance] that one may travel on Shabbos.

This is the eastern side. One might ask: From where does Rashi know this? One may explain that since west is called the rear one may infer that the front is the east. An alternative explanation: A hei at the end of a word is in place of a lamed at the beginning. Thus, since קדם means פנים (front — lit. face) it is clear that קדמה would mean לפנים (towards the front) while the word מזרחה would also mean towards the east. (Gur Aryeh) One might ask: Why does the Torah write the repetitive phrase קדמה מזרחה (in the forefront to the eastern side)? It appears that it wishes to teach us that because Yehudah held the kingship he was to be given the side that was most important. Therefore the east was referred to in terms of being “first” and “in the forefront.” If the Torah had written מזרחה or קדמה alone we would not have learned this point.

When they see the cloud. Rashi is answering the question: How did they know when to travel in order that they would be first to travel. For one cannot say that they traveled at their own volition, since the Torah writes “on the word of Hashem did they travel” (Bamidbar 9:18). Thus Rashi explains, “When they saw the cloud…” Re’m writes that one might question: Why does Rashi omit Moshe’s declaration “Arise Hashem…” (Bamidbar 10:35) and only mention the lifting of the cloud and the blowing of the trumpets? It appears that Rashi only comes to explain how they knew to prepare themselves to travel, and he says that they knew this “when they see the cloud rise.” However, the actual journey was not until Moshe said “Arise Hashem.” Thus when the verse writes “they travel first” it means that they were the first to prepare themselves to travel. I will write more about this in Parshas Beha’aloscha (ibid). (Nachalas Yaakov) I myself say that Rashi omitted this, because in Parshas Beha’aloscha he also brings the Beraysa on the verse “on the word of Hashem did they travel” (Bamidbar 9:18), and that they traveled in response to three things. (See Rashi Bamidbar 1:2) See there.

The way they camped. This is according to the view that they traveled in the shape of a box. The explanation of the term “gatherer for all of the camps” (Bamidbar 10:25), that is written concerning Don, means that if anyone from the tribes who had already traveled lost something, Don would return it to them. However, Rashi does not mean to say that the banner of the tribe of Don was the very last of all the banners, in accordance with the opinion that they traveled in the shape of a beam.

After those two banners. Meaning that “in the center of the camps” refers to the four camps of Israel, two in front and two behind. But it does not mean that it was between the camps mentioned above (vs. 3-16), i.e. between the camps of Yehudah and Reuven, given that it is written “the Tent of Meeting shall travel” after [mentioning] the banners of Yehudah and Reuven.

As Targum translates “the one near him.” Previously (v. 5, 12) Rashi did not need to explain the word עליו (with him, lit. “above him”) because the Torah added the words “those who camp.” Thus it was obvious that the explanation is as Targum translates. However here where it does not add anything, but merely states “along with him is the tribe of Menashe,” I would not know the meaning of the word ועליו, therefore Rashi explains “as Targum translates.”