Okay, l need help figuring this out.
If you start at a company on January 1st.
And you know you will accrue 12 business days vacation time over the next twelve months, but if you leave mid October, how many vacation days would you be paid for?

That would depend on company policy - most places they are not legally required to pay you for ANY of them. But if they do, and many companies do, they'd probably pay for nine, for the nine full months that you worked, if the policy is that you accrue one day per month. If the policy is that you accrue 12 per year, you might not have any accrued since you did not work the full year

That depends on the regulations of where you live. Some states require it to be prorated (you would get 9 days). Others use the logic that you receive 12 days after twelve months. Since you have not been there for 12 months, you would not be entitled to any. Your employee handbook should cover this. Or check with your states Department of Labor.