In Num 4:49, we read:
According to the
commandment of the Lord they were numbered by the hand of Moses
(בְּיַד־מֹשֶׁ֔ה), every one
according to his service, and according to his burden: thus were they numbered
of him, as the Lord commanded Moses.
While not impossible, I doubt that Moses
alone numbered the 8,580 men from v. 48. This shows us that "by the hand
of 'x'" does not mean literally, but it has also the sense of doing an
action on behalf of someone (in this case, Moses) (cf. "by the hand of Abraham").