The paper presents the results of experiments on measuring the cross sections for elastic scattering and nucleon transfer channels in the 6Li+9Be reaction at an incident energy of 68 MeV: 9Be(6Li,6Li)9Be, 9Be(6Li,7Li)8Be, 9Be(6Li,7Li)8Be2+, 9Be(6Li,8Li)7Be, 9Be(6Li,7Be)8Li. The aim is to reveal the manifestation of the cluster structure of 9Be. Theoretical analysis of the contributions of one-step and two-step neutron transfer mechanisms is performed using the distorted wave Born approximation method with the Fresco code. Good agreement between the calculations and the experimental data was obtained for the channels of elastic scattering 9Be(6Li,6Li)9Be, neutron 9Be(6Li,7Li)8Be and proton transfer 9Be(6Li,7Be)8Li, as well as the transfer of two neutrons 9Be(6Li,8Li)7Be. It is shown that the dineutron cluster transfer mechanism makes a dominant contribution to the 9Be(6Li,8Li)7Be reaction channel at forward angles.