When did the Messenger of Allah fast six days of Shawwaal?
All perfect praise be to Allah, the Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His Slave and Messenger.
There is no doubt that fasting six days in the month of Shawwaal is a confirmed act of Sunnah. It was narrated on the authority of Abu Ayyoob Al-Ansaari, may Allah be leased with him, that the Prophet said: "Whoever fasts Ramadan and follows it with (fasting) six days in Shawwaal, it is as if he fasts the whole year." [Muslim]
Nothing was mentioned in the practical Sunnah about the way the Prophet used to fast the six days of Shawwaal. Moreover, there is nothing in the Sunnah that indicates that the Prophet observed fasting these six days or not, and this is therefore open to either possibility. We can neither confirm nor negate a certain action unless there is a confirming or negating Sharee‘ah text.
To consider a certain act as a part of Sunnah, it is not necessary that it be proven by both the verbal and practical Sunnah of the Prophtet . Rather, there are some acts of the Sunnah which the Prophet did despite the fact that there are no relevant verbal statements, such as the Sunnah of I‘tikaaf (ritual seclusion in a mosque), for although there is not even a single authentic Hadeeth to indicate its virtue, it is established with full certainty that it is part of the Sunnah because the Prophet constantly observed it.
Similarly, some acts of the Sunnah were verbally and not practically established. The Prophet might have abandoned a certain act due to some reasons or to indicate that it is permissible to abandon it, such as the Dhuhaa (forenoon) Prayer. In an authentic Hadeeth, ‘Aa’ishah, may Allah be pleased with her, said that she did not see the Prophet performing it. However, the Hadeeths which encourage Muslims to perform it reach the highest degree of authenticity.
If we suppose that the Prophet did not observe fasting the six days of Shawwaal, he might have not done so for the aforesaid reasons.
To conclude, the majority of scholars are of the view that it is recommended to observe fasting six consecutive days of Shawwaal immediately after Ramadan.
Allah Knows best.