From BlackBiJewess‬ (@blackbijewess.bsky.social‬):

Question:
How did people track dates BCE?
That term helps us but certainly wouldn't have been used then
Did they count time like in the Bible when they say things like
"4th year in the reign of King Josias"
Or similar?

There were a few ways in which folks determined years and those ways did not develop in a linear fashion. For the first millennium, many societies used "Year [X] of (the reign of) [Royal Name]." That seems to have been in vogue until the Seleucid period (it turns out that empires can control time).

That first millennium style was influenced by an earlier "limmu" calendar system. Limmus were elected officials that held annual civic duties. For example, if you knew the limmu's name when you filed a lawsuit, you knew the year. At some point, kings adopted this system into their own elections.

Folks in Babylonia didn't use the limmu system, they had year-names based on royal activities: 

"The year King Samsu-iluna destroyed Kisurra and Sabum"; or, 

"The year King Rim-Sin built the great city wall of Iškun-Šamaš on the bank of the Euphrates."

As you might imagine, this can get tricky.

Year names were often long and subsequently abbreviated; some years had multiple names; some cities flipped between competing kings and their records reflect that political fence straddling. Funnily enough, David Foster Wallace borrowed this confusing style for his book, Infinite Jest.

Recording and tracing chronology is one of the most difficult aspects of ancient history, as it requires a wild amount of data, including sciences like astronomy and radiocarbon dating. Moreover, all of the above assumes we have known data from then to now and we don't: there were dark ages.