According to the commandment of the LORD through Moses they were listed, each one with his task of serving or carrying. Thus they were listed by him, as the LORD commanded Moses.
We have here a particular account of the numbers of the three families of the Levites respectively, that is, of the effective men, between thirty years old and fifty. Observe, 1. The Kohathites were, in all, 8600 from a month old and upwards; but of these there were but 2750 serviceable men, not a third part.
Commenting on Numbers 4:34-49
According to the commandment of the LORD they were numbered by the hand of Moses, every one according to his service, and according to his burden: thus were they numbered of him, as the LORD commanded Moses. (x) So that Moses neither added, nor diminished from that which the Lord commanded him.
Num 4:49 “According to the commandment of Jehovah, they appointed them through the hand of Moses (i.e., under his direction), each one to his service, and his burden, and his mustered things (פּקדיו), i.e., the things assigned to him at the time of the mustering as his special charge (see Exo 38:21).