Final answer:
The Babylonians used a sexagesimal counting system for general numeracy and astronomy, and another system for their calendar to assist in agriculture.
Step-by-step explanation:
The Babylonians used two main systems for counting: one was a sexagesimal (base-60) system for astronomical calculations and general numeracy which gave us the 360 degrees used in geometry and timekeeping that used a 60-second minute. The other system was used for their calendar that helped in agricultural planning, similar to the systems developed by other cultures like the Egyptians and Chinese who tracked celestial events for seasonal cycles.