The thermodynamic and magnetic properties of the mixed-spin (1/2-1) hexagonal Ising nanowire (HIN) system with core-shell structure have been presented by means of the effective-field theory (EFT) with correlations. The effects of the physical parameters of the system on thermodynamic and magnetic properties (magnetisations, susceptibilities, internal energies, free energies and hysteresis curves) are investigated for the both ferromagnetic and antiferromagnetic case, in detail. One can find that when the temperature increases the hysteresis loop areas decrease and the hysteresis loops disappear above the critical temperature. Moreover, different hysteresis loop behaviours have been observed such as single, double and triple hysteresis loops in the system. In order to confirm the accuracy of the phase transition points, we also investigate the free energy of the system.