I am currently researching about dhul hijjah and have not read what days specifically you are meant to fast, is anyone able to shed some light?
In general you could fast all the month except the day of 'Id (10th dhil Hijja):
'A'isha (Allah be pleased with her) said that the Prophet (ﷺ) forbade to observe fast on two days-the day of Fitr and the day of Adha.
[Sahih Muslim and other Versions in Sahih al-Bukhari etc.]
And you could fast as usual mondays and thursdays and all the days which are recomanded in any other month in general.
But you should also be aware that in this special month during the 11th, 12th and 13th (the so called days of tashreeq) optional voluntary fasting is considered as haram by the majority of scholars except for those people who perform hajj tamatu' and can't afford hady as stated in (2:196) and due to many narratives saying:
- Narrated Uqbah ibn Amir: The Prophet (ﷺ) said: The day of Arafah, the day of sacrifice, the days of tashriq are (the days of) our festival, O people of Islam. These are the days of eating and drinking.
[Sunan abi Dawod and other Versions in other Sunan Books]
- Nubaisha al-Hudhali reported Allah's Messenger (ﷺ) as saying: The days of Tashriq are the days of eating and drinking.
- It was narrated from Abu Hurairah that the Messenger of Allah (ﷺ) said: “The days of Mina (11th, 12th, and 13th of Dhul-Hijjah) are days of eating and drinking.’”
[Sunan ibn Majah]
- Abu Murrah, the client of Umm Hani, entered along with 'Abd Allah b. 'Amr upon his father 'Amr b. 'As and he brought food for him. He said: Eat. He said: I am fasting. 'Amr said: Eat, these are the days on which the Messenger of Allah (ﷺ) used to command us to break fast, and forbid us to keep fast. The narrator Malik said: These are the day of al-tashriq (i.e. 11th, 12th, and 13th of Dhu al-Hijjah).
- Narrated 'Aisha and Ibn 'Umar:
Nobody was allowed to fast on the days of Tashriq except those who could not afford the Hadi (Sacrifice).
As for fard fasting (qada'/making up days of Ramadan or kafara etc.) the matter is discussed, but still most scholars regard fasting in these cases as not permisible.
But it's recommanded at least to fast the day of 'Arafa (9th dhil Hijja) and if possible the whole first 9 days.
And Allah knows best