It is commendable to keep six fasts in the month of Shawwal. The Prophet, Sall-Allahu alayhi wa sallam, has said:
Whoever completes fasts of Ramadan then adds to them the fast 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. 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 2nd of Shawwal and keep fasting up to the 7th of it. However, if, they are kept in other days, it is hoped that the requirement of the above hadith may also be fulfilled.