After Ramadan, comes the month of Shawal. We fast six days during this month. It is Sunnah and not obligatory. According to Hadeeth, (who he fasts Ramadan and follows that with six days in Shawal, it is as if he fasts forever.)
This is built on one good deed equals that ten times the same. so the idea is like this. Ramadan is thirty days. if you multiply all that by ten, it equals three hundred days. the six days of Shawal are consequently sixty days. That makes a total of three hundred and sixty days. The number of days in a year. I am doing that at the moment and many other Muslims in different parts of the world are doing the same.
The six days are not necessarily in order. You can fast on the second day of Shawal and then take the fourth or the eighth day. I prefer doing that in one go because my digestive system is accustomed to fasting since the month of Ramadan. Once more, happy Eid to you.