I also calculate six months from August as 8+6=14mod12. I wonder if anyone does it differently, this seems like the most plausible technique.
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.
Never sure why I did this association, maybe it comes from a drawing in a book I read when I was six or somthn?