We report on the detailed characterization of the HD 77946 planetary system. HD 77946 is an F5 (M=1.17M_{sun}_, R=1.31R_{sun}) star, which hosts a transiting planet recently discovered by NASA's Transiting Exoplanet Survey Satellite (TESS), classified as TOI-1778 b. Using TESS photometry, high-resolution spectroscopic data from HARPS-N, and photometry from CHEOPS, we measure the radius and mass from the transit and radial velocity observations, and find that the planet, HD 77946 b, orbits with period Pb=6.527282-0.000020_^+0.000015^d, has a mass of Mb=8.38+/-1.32M_{Earth}, and a radius of Rb=2.705-0.081_^+0.086^R_{Earth}. From the combination of mass and radius measurements, and the stellar chemical composition, the planet properties suggest that HD 77946 b is a sub-Neptune with a ~1 per cent H/He atmosphere. However, a degeneracy still exists between water-world and silicate/iron-hydrogen models, and even though interior structure modelling of this planet favours a sub-Neptune with a H/He layer that makes up a significant fraction of its radius, a water-world composition cannot be ruled out, as with Teq= 1248^+40^-38_K, water may be in a supercritical state. The characterization of HD 77946 b, adding to the small sample of well-characterized sub-Neptunes, is an important step forwards on our journey to understanding planetary formation and evolution pathways. Furthermore, HD 77946 b has one of the highest transmission spectroscopic metrics for small planets orbiting hot stars, thus transmission spectroscopy of this key planet could prove vital for constraining the compositional confusion that currently surrounds small exoplanets.