Six fasts of Shawwal (Shawal Kay Rozay)
The Holy Prophet Sallallaho Alaihi Wasallam Has stated that those who have kept the fasts of Ramadan and then kept six fasts of Shawwal, then they are like those who have always kept a fast. He has also stated that if you fast after Eid for six days then you have fasted for the whole year
[Muslim, Abu Da'ud Tirmizi, Nisaai, Ibne-Maja etc.].
It is better that they are kept. separately and if they are kept continuously after Eid then there is no harm [Durr-e-Mukhtar, Bahar].