The cross sections for the production of nuclides of element 108 via hot fusion evaporation reactions are studied using a two-parameter Smoluchowski equation. The optimal reactions for the synthesis of new nuclides of element 108 with mass numbers from 266 to 271 are suggested. The macroscopic-microscopic approach predicts a strong deformed shell closure at Z ≈ 108 and N = 162. The synthesis of more nuclides of element 108 is meaningful to the confirmation of the existence of this deformed shell closure.