How to get admission in class 12

He passed SSC 2004. That is 16 years back. Now he wanted to study further. He can do that. There are many ways to study further. He can get admission into any open university and do a degree of his choice. He need not do the first 12th class and then a degree. He can directly write an entrance test and join in a degree course in any open university or any distance mode education. He can select the subjects he is interested in and do the course. There are many universities offering distance more of education and open university classes. Advise him accordingly.

Since your cousin has passed class ten from CBSE Board in 2004 and is interested to complete class twelve. The same can be achieved in the following manners-
1) You may advise your cousin to meet the Principal of the school from where he has passed out class ten CBSE Board and apprise the Principal of his his desire to continue class twelve as a private candidate. In case of his acceptance, you can proceed your studies. Being as a private candidate, attendance clause of securing at least 75 percent will not be applicable in your case.
2) On the basis of your passing out Class ten CBSE, your cousin may get his name enrolled for class twelve conducted by IGNOU. Studying the materials provided by the IGNOU authority, you cousin can clear the class twelve examination conducted by IGNOU. IGNOU has wide acceptance in terms of recognition of the course from the different educational institutions apart from its acceptance for the job purpose not only in India but even from the abroad as well.
3) You may advise your cousin to take up the degre course either from IGNOU or from Karnataka Open University with the clearance of admission test required for this purpose and your cousin take up graduation course of his choice. In that way, he will be exempted for appearing class twelve test. He has to write the papers meant for the degree course of his choice. This degree will have recognition for both academic and service sectors.

Nowadays there are many options and alternatives one has got to study and give exam for class 12 after a gap after completing class 10. The easiest would be to apply for 12th exam as a private candidate. A private candidate does not attend school and has no need of some school attendance to appear in the exam. It is understood that the private candidate has studied the syllabus and he is ready to appear in the exam. So one has to apply for appearing in exam as a private candidate by depositing the required fee and filling the form. The details can be obtained from the relevant college in the place where the student wants to appear in the exam.
Most of the students who have not in touch with the schools go for this mode.

Another thing is there is a provision of Bachelor Preparatory Programme (BPP) conducted by some distance universities like IGNOU and Dr. Babasaheb Ambedkar Open University. This is a course which can be done by those who have not done class 12 due to some reasons. Once they do BPP then they can do B.A. or B.Com. from these distance universities. So, BPP facilitates some people to go for graduation from these distance institutions. At the same time BPP is not equivalent to 10+2. Which means that if the eligibility for some engagement is 10+2 the BPP qualified person cannot claim his candidature there. IGNOU offers preparatory course in Commerce, Mathematics and Social Sciences. The course duration range from 6 months to 2 years depending upon the performance of the student. There is minimum age of 18 years for admission but there is no maximum age limit.

He can pursue the course from the open universities also, because in open boards there is no need to maintain attendance , just complete some assignments assigned by the board and you will get promoted.
Also there are many private institutions which provide such facility.
So according to your choice you can approach anyone of them.