Numbers 3:14-20 meaning

Again, the Lord spoke to Moses in the wilderness of Sinai. He told Moses to number the sons of Levi by their fathers' households, by their families, and he was to count every male from a month old and upward. This was different from how he numbered the males in the other tribes. Moses counted the Levite males "a month old and upward," whereas with the other tribes he counted "twenty years old and above" (Numbers 1:20). The difference was that males counted in the other tribes were limited to those twenty and older, because only those twenty and older were eligible to serve in the military. Here, the Levites were numbered according to the total number of males older than one month of age. So, in obedience, Moses numbered them according to the word of the Lord, just as he had been commanded.

The Levites were descended from the sons of Levi and were numbered by their names, which were Gershon and Kohath and Merari (Genesis 46:11, Exodus 6:16). Thus, the divisions within the tribe of Levi were ordered and organized according to Levi's three sons, and were numbered accordingly. Moses then named the descendants of each son of Levi. First, he lists the names of the sons of Gershon, Levi's firstborn, by their families (v. 18), which were Libni and Shimei (Exodus 6:17). Next, the sons of Kohath, Levi's second born, were counted by their families, which were Amram and Izhar, Hebron and Uzziel. Amram was the father of Moses, Aaron, and their older sister Miriam (Exodus 6:20, Numbers 26:59, I Chron. 6:3). Then, the sons of Merari were numbered by their families, whose names were Mahli and Mushi.

So, the census would be taken based on the families of the Levites according to their fathers' households. No reason is given here for the method of numbering the Levites other than it was what the LORD commanded.