Six Fast Shawwal Month Hadith Sahih Muslim Merits Fazail virtues

Six Fasts in the Month of Shawwal
It is commendable to keep six fasts in the month of Shawwal. The Holy Prophet SAWhas said:
“Whoever completes the fasts of Ramadhan then adds to them the fasts of six days in the month of Shawwal, it will carry the thawab of fasting for the whole year.” (Sahih Muslim)

This Hadith had described the great thawab of six fasts of this month. 
The scholars have interpreted this Hadith by saying that according to the recognised rules of Shari‘ah, every good deed is rewarded ten times more thawab of its origin, therefore, the thawab of 30 days of Ramadhan amounts to the thawab for 300 days. If the fasts of Ramadhan are followed by six more fasts, they carry the thawab of 60 days more, raising the aggregate thawab to 360 which is the number of dais in one year according to the Islamic calendar. 
Therefore, the Muslims should take this opportunity of acquiring such an enormous reward from Allah. 
It is more preferable to start these fasts from the 2 nd of Shawwal and keep fasting up to the 7 th of Shawwal. However, if they are kept in other days, it is hoped that the requirement of the above Hadith may also be fulfilled.
source: Darul Uloom Bury, United Kingdom