All perfect praise be to Allah, The Lord of the Worlds. I testify that none is worthy of worship except Allah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and messenger.
We ask Allah, The Almighty, to accept his repentance and forgive him, for neglecting fasting without a valid excuse is one of the major sins. We seek refuge with Allah from this.
Now, the situation of your father must be one of following two cases:
Firstly, he is unable to fast at all, due to his old age. In this case he is not obliged to fast nor make up for the missed months of fasting. However, he is required to feed one poor person a mudd (approximately 750 ml) of foodstuff for each day that he missed. He should do this for the four months instead of making up for them and offer the same amount as expiation for delaying making up for them until this time.
If Ramadan comes and he is not able to fast, then he is not obliged to do anything except feed a poor person for each day, according to what was previously stated.
Secondly, he is able to fast. In this case, he is obliged to make up for the four months. He can fast them separately, according to his ability. He is also obliged to feed a poor person a mudd of food for each day, as expiation of delaying making up for the fasts until now.
What you have stated regarding expiation and that it consists of fasting two months for each missed day is incorrect, unless he observed fast on a day and deliberately broke it by having sexual intercourse. In this case, he is required to fast two consecutive months, but if he cannot, then he has to feed sixty poor persons.
Allah Knows best.