What should I do to make up for the day I broke my fast after intending to observe a make-up fast on the fourth day of Eid al-Adha, knowing that fasting on that day is forbidden, and how many days do I need to fast in return?

We have previously clarified the ruling on making up missed fasts (qada') on days when fasting is prohibited, which include the days of Tashreeq. The summary of this is that fasting on these days is not permissible, even if it is for qada'. Therefore, your breaking of the fast on that day was correct and not considered intentionally breaking a qada' fast, because fasting on that day is not permissible. You are not required to make up that particular day, but only what you missed from Ramadan. It should be noted that intentionally breaking a qada' fast is not permissible.