We could consider half as old counted by days, leaving out leap day and counting by integer days. 4 years old is between 1460 days and 1824 days inclusive. That means the sister is between 730 days and 912 days inclusive.
You are between 1824-730=1094 days and 1460-912=548 days older than your sister. If your sister is 12 and just had her birthday, then you are at the minimum 13 (548 mod 365 = 1). If your sister's birthday is tomorrow, you are maximum 15 ((1094+364) mod 365 = 3). You could also be 14.
We could also consider half as old counted as integer years, again leaving out leap days and counting only integer days. Here you are 4 years old and your sister is 2 years old. So the max difference is you are 4 * 365 + 364 = 1824 and your sister is 2 * 365 = 730. So a difference of 1094 days. The min difference is you are 4 * 365 = 1460, your sister is 2 * 365 + 364 = 1094. So a difference of 366 days. This gives the same result as the above. Using the min difference on your sister's birthday makes you one year older. Using the max difference on the day before your sister's birthday makes you 3 years older.
BTW, if this is a pedantic thing about people born on leap year only having a birthday every 4 years, I swear...