Question 20: Is it obligatory to fast the six days of Shawwaal consecutively, or one may fast them separately during the month?
Answer: Observing Sawm (Fast) on six days of Shawwaal is a stressed Sunnah reported from the Messenger of Allaah (peace be upon him). It is permissible to observe Sawm on these days either consecutively or separately. The Messenger of Allaah (peace be upon him) generally urged us to observe Sawm during six days of Shawwaal, but he did not specify either consecutively or separately. He (peace be upon him) said: Anyone who fasts Ramadaan and then follows it with six days of Shawwaal it is as if they fasted the whole year. (Related by Imaam Muslim in his Saheeh [Authentic Hadeeth Book])... read more here.