Yes you are eligible If you are in 6th. Minimum eligibility criterion is 45-50%(Varies from university to university)in graduation (any stream) .Admission to the same is based on entrance exams like CLAT, LSAT, AILET etc. Some universities can consider you if you submit your full result of compartment after improvement exam. 

Admission Process: Admission is done either on the basis of marks obtained by candidates in qualifying degree or through entrance test.candidates also get direct admission into the same.

Before practicing in any court of India, LL.B. graduates have to obtain the “certificate of practice in law”. It can be obtained by giving the “All India Bar Examination (AIBE)” regulated and supervised by the Bar Council of India.you can work in:Legal Cells of Private and Public Sector CompaniesState Bar CouncilsConsulting FirmsIndian and Foreign Law FirmsLegal Department of Foreign CompaniesMulti National CompaniesGlobal Audit and Compliance FirmsJob Profiles for LLB Graduates:Public ProsecutorLegal AdvisorLegal ExpertAttorney GeneralAdvocateNotaryLaw ReporterMagistrateDistrict & Sessions judgeTeacher & LecturerMunsifs (Sub-Magistrate)TrusteeSolicitor

Best colleges for doing LLB are: National Law University, Jodhpur, ILS LAW COLLEGE - PUNE, National Law School of India University ,Bangalore, Gujarat National Law University, LOVELY PROFESSIONAL UNIVERSITY - JALANDHAR, THE WEST BENGAL NATIONAL UNIVERSITY OF JURIDICAL SCIENCES -KOLKATATHE NATIONAL LAW INSTITUTE UNIVERSITY - BHOPALSYMBIOSIS LAW SCHOOL -PUNEFACULTY OF LAW, BANARAS HINDU UNIVERSITY, VARANASIFACULTY OF LAW, UNIVERSITY OF DELHI, NEW DELHINATIONAL LAW UNIVERSITY - NEW DELHIMS Ramaiah College of Law, BangaloreChrist University, Bangalore,NALSAR University of Law, Hyderabad,