The month of Dhu al-Hijjah is one of the Hijri months that comes after the month of Dhu al-Qa`dah and before the month of Muharram so it is the twelfth month. That makes it the last month in the Hijri year.

In this holy month, God imposed the Hajj, which is one of the pillars of Islam, on His servants who are able to perform it.  God Almighty made the virtue of good deeds, worship, and fasting in these ten days more rewarding than any other day of the year. God swore by these ten days in Surah Al-Fajr “By the dawn(1) And [by] ten nights(2) And [by] the even [number] and the odd(3). In addition, the Prophet Mohammed peace be upon him told companions about its virtues when Ibn ‘Abbas (may Allah be pleased with him and his father) reported that the Prophet (peace and blessings of Allah be upon him) said: “There are no days in which righteous deeds are more beloved to Allah than these ten days.”

What are the good deeds and acts of worship that we can do in Dhu al-Hijjah?

During these days, a Muslim should strive to perform worship, such as prayer, reading the Qur’an, remembrance of God Almighty, seeking forgiveness, taking care of kinship ties, and other good things. And the most important thing is fasting in these days as it is mentioned in Sunan Abu Dawud that some of the Prophet wives said that He used to fast nine days of Dhu al Hijjah. Especially the fasting in Arafah Day has great reward, Abu Qatada al-Ansari narrated that Muhammad was asked about fasting on the Day of Arafah, whereupon he said: It expiates the sins of the preceding year and the coming year.

But the good question is why are the first ten days are the greatest?

It is because the principles of worship are combined in it, which are: prayer, fasting, charity, and Hajj, and this thing does not happen at any other day. The ten days of Dhul-Hijjah are also preferred in terms of days, as they include the Day of Sacrifice (tenth day) you can see Eid al-Adha.. Sacrifice, Rituals and Joys , the Day of Arafah (nineth day), and the Day of Tarwiyah (eight day), in which pilgrimages were used to drink and store  enough water to the last day of Al Hajj.  . As a result, all of that make these days better than any day in the year even the last ten days of Ramadan.

References

Islamweb.net أفضل الأعمال في عشر ذي الحجة

Islamweb.net فضل العشر من ذي الحجة