Fasting is haram (forbidden) on Eid al-Adha and the three days following it, totaling four days.
This prohibition is based on the hadith reported by Abu Hurairah, where the Prophet Muhammad (peace be upon him) stated, "You are not to fast these days. They are days of eating and drinking and remembering God." This specifically refers to the days of Eid al-Adha and the days of Tashreeq (the three days following Eid al-Adha).
Additionally, it is considered makrooh tahrimi (highly disliked, nearing haram) to single out Fridays for fasting regularly. While not strictly haram in the same sense as fasting on Eid days, repeatedly and exclusively fasting only on Fridays is discouraged.
Therefore, the exact answer to the question of how many days fasting is strictly haram is four days: Eid al-Adha and the three days following it.