Abū Ayyūb Al-Ansārī radhiyallāhu ‘anhu narrates that the Messenger of Allāh sallallāhu ‘alayhi wasallam said,
“If anyone keeps the fasts of Ramaḍān and follows them up with six fasts in Shawwāl, then it is like a year’s fasting.” (Muslim)
Allāh ta‘ālā mentions in the Glorious Qur'ān:
“Whoever brings a good deed shall get ten-fold the like of it.” (6:160)
Therefore, the fasts of Ramaḍān equate to 300 days, as 30 [fasts] x 10= 300 days, which is equal to 10 months. Then, by fasting the extra six days, one receives the reward of another 60 days as 6 [fasts of Shawwāl] x 10= 60, which is equal to 2 months. So, one earns the reward for fasting the entire year.
Note: These fasts can be kept after the day of 'Īd. It is also not necessary to keep them consecutively. They can be kept at any time during the month of Shawwāl. However, it is advisable to keep them immediately after the day of 'Īd as one will already be in the rhythm of fasting, thus, it will be easier.