Explanation:

29th Feb, 2016 = Monday => 28th Feb, 2012 = Sunday
28th Feb, 2017 = Tuesday (because 2016 is a leap year, there will be 2 odd days)
Therefore» Feb 28th 2018 (Wednesday), Feb 28th 2019 (Thursday), Feb 28th 2020 (Friday), Feb 29th 2020 (Saturday)
Or, Feb 29th to Feb 29th after 4 years, we have 5 odd days.
So, every subsequent birthday, would come after 5 odd days.
2020 birthday – 5 odd days
2024 birthday – 10 odd days = 3 odd days
2028 birthday – 8 odd days = 1 odd day
2032 birthday – 6 odd days
2036 birthday – 11 odd days = 4 odd days
2040 birthday – 9 odd days = 2 odd days
2044 birthday – 7 odd days = 0 odd days. So, after 28 years, his birthday would fall on Monday.
The next birthday on Monday would be in year 2072 (further 28 years later), the one after that would be in year 2100.

But we are told that she lives upto year 2099.
So, there are 2 occurrences of his birthday falling on Monday – 2044 & 2072.

Hence, option 2 is the correct answer.