I remind you all of the importance and desirability of fasting six days in the month of Shawwaal after Ramadaan. Prophet Muhammad (SAW) said: "He who observes As-Saum (the fast) in the month of Ramadaan, and also observes As-Saum (the fast) for six days in the month of Shawwaal, it is as if he has observed As-Saum for the whole year." [Recorded by Imaams Muslim and others]
Fasting during Shawwaal can be any six days during the month, after the day of Eid. These days do not have to be consecutive nor are they specific days.