I got 5946 rank in AP eamcet am I eligible for getting free seat .

Hello aspirant!
Well based on your rank you can get a seat in the following Colleges considering you belong to Open category.
1)RVR and JC College of Engineering-CSE .
2)JNTUA College of Engineering, Pulivendula-CSE.
3)A S K College of Technology and Management-CSE.
4)Adikavi Nannaya University-CSE.
5)JNTUA College of Engineering, Kalikiri-CSE.

Now coming to the point of getting free seat,well it depends on your rank,category,annual family income.As far as your rank is concerned it's good and if you belong to reservation category then you can get a free seat.

For further information refer to the following link:

http://www.careers360.com/ap-eamcet-college-predictor
Hope it helped!
All the best!