The Eid el fitr has been june 25th. I want to know if it is allowed to fast june 26th as a part of the 6 days (fast) of Shawal or sunna (Monday and Thursday). Thank you.
The first day of Shawaal is Eid-ul-Fitr but fasting is prohibited on this day. Therefore you can start it the day after. So you can start it on the second day of Shawaal.
This site has more info if you are interested.
You can start fasting six days of Shawwal from the second day of Shawwal, because it is haram to fast on the day of 'Eid. You can fast the six days at any time during Shawwal, although the best of good deeds are those which are done soonest.