How does this work with the rolling 180 days?
You entered on 11 June. In the 180-day period that starts with 11 June, you can only be present for 90 days. Of those 90 days, you used 13 with your first visit. That leaves you with 77 days to use in the period from 24 June (the day after you left) to 7 December (the last day of the 180-day period that starts with 11 June). This means that if you entered the Schengen area before 22 September, you will run out of days before the 180-day period ends, and your second visit will have to be shorter than 90 days (no more than 77 days, in fact).
If you entered on or after 22 September, your second visit can be up to 90 days long, because on any given day enough of your earlier presence will be more than 180 days old, so it will not count toward the 90-day total.
If the 90th day of your current visit is 8 December, that means you entered on 10 September. If that's true, then you have to count your days in June, and your 90th day is 25 November. In that case, you cannot stay in Italy until December, or even until 26 November.
If your 90th total day in the Schengen area is 8 December, that means you entered on 23 September, and you will hit the 90/180 limit on 21 December, so you must leave before the end of that day.
None of this applies, however, if you have a type-D Italian visa, because days of presence authorized by a type-D visa do not count for calculating the 90/180 rule.