Exchange mechanisms and magnetic structure in the two-dimensional cyano-bridged molecule-based magnet K2[Mn(H2O)2]3[Mo(CN)7]2.6H2O have been investigated by a combination of neutron diffraction studies on both single crystal and powder samples and theoretical DFT calculations. The experimental spin density has been deduced from a new refinement of previously obtained polarized neutron diffraction (PND) data which was collected in the ordered magnetic state at 4 K under a saturation field of 3 T performed in the C2/c space group, determined by an accurate re-evaluation of the X-ray structure. Positive spin populations were observed on the two manganese sites, and negative spin populations were observed on the molybdenum site, which provides evidence of antiferromagnetic Mo3+-Mn2+ exchange interactions through the cyano bridge. The experimental data have been compared to the results of DFT calculations. Moreover, theoretical studies reveal the predominance of the spin polarization mechanism in the Mo-C-N-Mn sequence, with the antiferromagnetic nature of the interaction being due to the overlap between the magnetic orbitals relative to manganese and molybdenum in the cyano bridging region. The magnetic structure of K2[Mn(H2O)2]3[Mo(CN)7]2.6H2O has been solved at low temperature in zero field by powder neutron diffraction measurements. The structure was found to be ferrimagnetic where the manganese and molybdenum spins are aligned along the axis in opposite directions.