Hadhrat Abu Ayub al- Ansari (radiyallahu anhu) reports that Rasulullah (sallallahu alaihi wasallam) said:
“Anyone who has kept the fasts of Ramadān and follows them up with six (optional) fast of Shawwal then (he will get the reward for the fast of a whole year, but if he does that always) it is as if he fasted all his life. (Sunan Abi Dawud, Vol.1, Pg330, HM Saeed)
Hadhrat Thaubān (radiyallahu anhu) reportes that Rasulullah (sallallahu alaihi wasallam) said:
“Joining six days of the fasts of Shawwal is equal to the fast of the whole year. Each good act is equal to ten such acts”. (Sunan Ibn Mājah, Pg.124, Dārul Qurān wal Hadith)
The reward of each good deed is multiplied at least ten times. Therefore, thirty days of fast in Ramadān equals three hundred days and the six fast of Shawwal equal sixty. Thus, totaling to three hundred and sixty days, which is the total amount of days in a lunar year.
(Sourced from the askimam.org website)