Which engineering branch can I expect in Manipal (main campus) with a rank of 4306?

You can get Aeronautical, Automobile, Biomedical, Biotechnology, Chemical, Civil, EEE, ICE, Mechatronics and PMT. For mechanical, you're on the edge. You might just get but may be in the last rounds. Other branches like CSE, IT, CCE and ECE may be quite difficult with this score. Still, you can try