[en] Double-differential cross sections and angular distributions of inelastic neutron scattering on ¹²C, ⁵⁶Fe, ⁸⁹Y and ²⁰⁸Pb have been measured at 96 MeV at The Svedberg Laboratory, Uppsala, Sweden. Results on elastic neutron scattering at 96 MeV from these nuclei have been reported previously. To obtain the inelastic cross sections, a forward-folding technique has been applied. A physically reasonable trial spectrum has been folded with the response function of the detector system and the output has been compared with the experimental data. To create the trial spectrum, a Gaussian has been used for the elastic part and the PRECO code for the inelastic part. Other models were tested for the pre-equilibrium contribution and the method was found to be model independent. The response function of the detector setup has been obtained experimentally at the smallest possible angle, in this case at 9 deg. The resulting inelastic scattering data cover an excitation energy range up to 45 MeV and the angular intervals 28 to 58 deg for ¹²C, 26 to 65 deg for ⁵⁶Fe and 26 to 52 deg for ⁸⁹Y and ²⁰⁸Pb. The results are discussed and compared to several model codes as well as existing experimental data for (n,n'x), (n,p'x) and (p,p'x)