All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
The Prophet said: “Whoever fasts during the month of Ramadan and then follows it with six days of Shawwal will be [rewarded] as if he had fasted the whole year.” [Muslim]
In another Hadeeth the Prophet said: “Whoever fasts six days after Eed al-Fitr will be rewarded as if he had fasted the entire year. Whoever does a good act he will be rewarded ten times.” [Ibn Maajah, and Shaykh Al-Albaani graded it as authentic]
The reward is for the one who fasts the entire month of Ramadan and then fasts six days of Shawwal. Therefore, you should make up the missed days of Ramadan first, and then fast the six days of Shawwal.
Allah knows best.