Shaykh Abdul-Aziz ibn Baz (rahimahullah):

In the Name of Allah, the Most Merciful, the Bestower of Mercy. All praise is due to Allah, and may Allah’s peace and blessings be upon the Messenger of Allah, and upon his family, his companions, and whoever is guided by his guidance. To proceed:

The Virtue of Fasting the Six Days of Shawwal

It has been authentically reported from the Messenger of Allah ﷺ that he said: “Whoever fasts the month of Ramadan, then follows it with six days from Shawwal, it will be as if he fasted the whole year.” This was narrated by Muslim in his Sahih. This indicates the virtue of these six days, and that fasting them along with Ramadan is like fasting the entire year. And this is a tremendous virtue.

Ramadan counts as ten months, and the six days count as two months since each good deed is multiplied tenfold. So it is as though he fasted the entire year. And on top of that, Allah, out of His kindness, Exalted and Most High, made Ramadan an expiation for what lies between the two Ramadans (i.e., from one year to the next). As for the six days, they are an added goodness, a tremendous benefit, and a great advantage in obeying the command of the Prophet ﷺ, in following his guidance and encouragement, and in being keen to do what Allah has legislated of acts of worship. This is a great good, and the believer seeks what Allah has legislated, and follows it seeking reward from Allah. There is tremendous reward in this.

When to Fast in Shawwal (Consecutive Days or Spread Out)

The six days do not have specific days assigned to them. Rather, the believer may choose any days throughout the month. If he wishes, he may fast them at the beginning of the month. If he wishes, he may fast them in the middle. If he wishes, he may fast them at the end. And if he wishes, he may spread them out — some at the beginning, some in the middle, and some at the end. The matter is broad and flexible, and all praise is due to Allah. If he hastens to them and fasts them consecutively at the beginning of the month, then that is better, as it is hastening toward good. But there is no restriction in this, all praise is due to Allah. The matter is flexible; if one wishes, he may fast them consecutively, and if he wishes, he may spread them out.

Not an Annual Obligation

If a person fasts them in some years and leaves them in others, there is no problem because they are voluntary fasts, not obligatory. So if he fasts them in some years and does not in others, or if he fasts some of the six and leaves some, there is no sin upon him, and all praise is due to Allah.

Source: Nur ala al-Darb (no. 120 & 826) — Access on the Shaykh’s website here and here