To calculate +/- 3/6/9 months I shift by seasons. 3rd month of summer becomes 3rd month of winter.

That works well cause all months live in a primitive memory palace in my head: an analogue clock face with July at 12 and January at 6. So shifting by 6 means rotating the clock hand from 11 to 5 and immediately visualising what month it falls on.

This might sound inefficient to an LLM but human brains had image processing before language.