Is it permissible for a young man to make up the days he missed in Ramadan due to masturbation in Shawwal with the intention of both making up the fast (qada') and observing the six days of Shawwal (siyam al-sitt) concurrently, and is this valid according to the Shafi'i school of thought?

Some scholars have permitted combining the intention of making up for missed Ramadan fasts with fasting the six days of Shawwal. Some Shafi'i jurists mentioned that whoever fasts to make up for missed days in Shawwal will attain the basic reward of fasting the six days, even if it is not complete, while some Shafi'is prohibited combining intentions in this matter.

As for the questioner, he must sincerely repent for intentionally breaking the fast during Ramadan, abandon the sin, associate with the righteous, and strive in supplication and remembrance of Allah Almighty.