In such circumstances two terminilogies are used in eudcational circles
1.Re-appearing: a candidate has failed in a particular subject and then has taken the exam once more.
2.Improvement: a candidate who has passed in all subject but has taken the exam once more to improve the scores.
In CBSE, the improvement exams is valid only if taken in the year after the first result. This is correct in your case. Most boards and insitutions will consider the best of the two as the final score.
The other important fact is that when a candidate takes exams from two boards during the same academic year (state and CBSE), then it becomes illegal.
Some boards have clear information, for instance in Maharastra, it is called as CIS - class improvement scheme wherein the student can take a call on retaining one marks card (https://timesofindia.indiatimes.com/city/pune/HSC-students-can-attempt-exam-twice-under-class-improvement-scheme/articleshow/17201298.cms).
Your case sounds more like you have done you regular XII in 2011 and then as a private candidate taken improvement exam in 2012. Does your second marks sheet have the mention of improvement. Have you got a reciept from 2012 which says you have paid the fees and reason for re-appearing as ímporve marks'?
This should be fine, I would suggest you verify it from your Bihar board or the college you studied or appeared for the second time, the administration staff would be handling such queries more often. You can use your 2012 XII card but be prepared to explain to the authorities about the gap.