An analysis of the available experimental data on the fusion and fission of the nuclei of (286)112, (292)114, and (296)116, produced in the reactions Ca-48+U-238, Ca-48+Pu-244, and Ca-48+Cm-248, as well as experimental data on the survival probability of those nuclei in evaporation channels with three- and four-neutron emission, enables the quite reliable conclusion that the fission barriers of those nuclei are really quite high, which results in their relatively high stability. The lower limits that we obtained for the fission barrier heights of (283-286)112, (288-292)114, and (292-296)116 nuclei are 5.5, 6.7, and 6.4 MeV, respectively.