In an authentic narration in Sahih Muslim, Prophet Muhammad said:
( مَنْ صَامَ رَمَضَانَ ثُمَّ أَتْبَعَهُ سِتًّا مِنْ شَوَّالٍ كَانَ كَصِيَامِ الدَّهْرِ )
“Whoever fasts Ramadan then follows it with six days of Shawwaal, it will be as if he fasted a lifetime.”
To make sense of the aforementioned hadith, The Prophet explained this when he said: “Whoever fasts for six days after (Eid) al-Fitr has completed the year: (whoever does a good deed will have ten good deeds (10x) like it).” According to another report: “Allah has made for each good deed ten like it, so a month is like fasting ten months, and fasting six days (6 days x 10 = 2 months) completes the year.” (Saheeh al-Targheeb wa’l-Tarheeb, 1/421). It was also narrated by Ibn Khuzaymah with the following wording: “Fasting for the month of Ramadan brings the reward of ten like it, and fasting for six days brings the reward of two months, and that is the fasting of the whole year.”
Watch the following video below for more encouragement and information about these 6 days.