What is the ruling on delaying the making up of 16 days of Ramadan fasting for six years due to studies, knowing that the delay was involuntary, and that the total she owes now is 30 days, and she fasted 13 days last year but was unable to complete them?

The usual hardship and toil of studying is not considered a valid excuse for breaking the fast in Ramadan (definition) unless it causes the fasting person unbearable difficulty. This applies to the ruling on those who perform arduous work; the general principle is that fasting is obligatory for them, but if they suffer unusual harm, they may break their fast to the extent necessary to alleviate that harm, and then make up the missed fasts.

Whoever breaks their fast due to a valid excuse (such as inability to complete the fast or illness) is not sinful and must make up the missed fasts. If they delay making up the fasts due to an excuse, they only need to make them up after their excuse is gone. However, if they delay it without an excuse until another Ramadan begins, they have sinned and must make up the missed fasts along with feeding a poor person for each day. This feeding is not repeated if the making up of fasts is delayed for more than one Ramadan.

Whoever owes missed fasts must hasten to make them up at suitable times, such as holidays, and not procrastinate or be lenient in this regard.