Mufti Menk encourages the audience to fast 6 days in the month of shawwal. The month of Shawwal is after Ramadan.
It is recommended you fast for 6 days to get the reward of fasting the whole year! That is if you have fasted all the days of Ramadan, if you missed any , this month is the month to make up for them with 6 extra.
After this you should continue to fast throughout the year because fasting has an immense reward with Allah. Allah says Fasting is for me and I will award it accordingly, fasting on Mondays and Thursdays is sunnah.