Which year of passing should be considered if the intermediate exam is given twice from Bihar Board?

Normally academic consideration is only latest. In your case the improvement examination passing date will be considered as year of passing. In such cases where one paper of the degree or higher secondary or intermediate appear subsequently for failure with lower marks of passing minimum or for improvement the later date only will be considered though passing other papers in the previous year.

You passed the 12th class from the Bihar board in the year 2018. But you scored less percentage of marks. So again you attended the same exam from the same board in the year 2019 for improvement. But you have not mentioned whether there is any improvement or not in the marks.
However, you can use any one of the above two certificates when you are applying for a job. But you should mention the year of passing as per the certificate you are using.

You have appeared for 12 th class Bihar Board initially in the year 2018 and again in view of your better performance , you appeared again in 2019 for the same class from Bihar Board. However, you have not indicated how you have performed your examination in 2019. There might be two cases in such an attempt. If your scores are less in 2019, the same scores will be treated as valid and so is the case of your higher marks, it would be treated as your final result.
In all the situations, results of 2019 would be final.
However in all the cases, you need to show the results of both the year - 2018 & 2019 specifying the details of marks of both the years if you appeared in some of papers for improvement. If you have appeared for the all the papers in the next year, you need not mention the results of the two consecutive years. In that case, your scorings of 2019, would be reckoned as your final result.

As mentioned above, you appeared for the 12th class from the Bihar board in the year 2018. But due to securing less percentage of marks, you tried again to attend the same exam from the same board in the year 2019. But, you did not mention here whether you secured more marks or not. As per my suggestion, you should apply that mark sheet for job purposes in which you secured more marks. There are some sort ituations. If you appeared for some paper for marks improvement then your passing year would be 2019. And If you appeared for the exam on all papers then you should use that mark sheet in which you secured more marks. The

Now, you have got two marksheets for your class 12 final exam secured in the year 2018 and 2019 respectively. It is obvious that you have to present the marksheet which is showing more marks and corresponding year will become the year of completion.
If you present the 2019 results then you might have to explain your engagements during 2018 as not mentioning that will be treated as a gap year in your career. On the other hand if you present your 2018 result then 2019 will become a gap year. To explain this gap you will have to attach the marksheet of both the years. But the year will be the one which you claim in preference and mention in the application form wherever you apply.