If penicillin is considered to be active against only gram positive organism and how penicillin g treats meningitis caused by neisseria meningitis?

PCN can treat gram negative organisms too as you have known about using PCN for N. meningitidis or N. gonorrhoeae which are gram negative diplococci.

A good question. Not all gram negative organisms are resistant to penicillin. Both Neisseria meningitidis and gonorrhea have sensitivity to penicillin, though there is greater prevalence of resistance to penicillin for gonorrhea. Even 10% of E coli are sensitive to penicillin. There are exceptions to usual rule of gram negative organisms not being sensitive to penicillin. like most rules.