The continuous neutron spectrum from the t→d+n breakup reaction can best be extracted in the 3H(p,n)3He and 4He(t,n)6Li reactions because of minimum neutron background in both cases. Only for the latter reaction are neutron background spectra also available. These data were measured at 11.88-MeV triton energy at eight angles between 0 and 120 deg. As a test for the validity of the procedure, angle-dependent differential cross sections of 4He(t,n)6Li were extracted and converted to 6Li(n,t)4He at En = 2.32 MeV by detailed balance calculation thus contributing to the R-matrix analysis of the 7Li system. The double-differential and neutron energy integrated cross sections at that energy are given as well as those for the triton breakup of the time-reversed reaction.