Is it permissible to give money to the needy instead of fasting the remaining six days of the past Ramadan's make-up fast, or is it obligatory to fast them?

The questioner is obligated to make up for the days she missed fasting. Feeding the poor is not a substitute for making up the fast unless one is unable to fast due to an incapacity that is not expected to cease. The missed days must be made up before the next Ramadan begins. If Ramadan arrives before the missed days are made up, then they must be made up after it, and the obligation to make them up is not waived by delay. If the delay was due to a valid excuse, then only making up the fast is required. If the delay was without a valid excuse, then along with making up the fast, one must feed a poor person for each day, unless she was unaware of the impermissibility of delaying, in which case the expiation (feeding) is waived.