Question

is on can be the answer of this question - you can obtain the answer -------- adding the date of birth to this date

Answer 1

No, 'on' will be wrong answer. The most appropriate preposition in this blank will be 'by'.

You can obtain the answer by adding the date of birth to this date. Here the meaning of 'by' is 'Through the means of'. 

Answer 2

You can obtain the answer by adding the date of birth to this date.