The six-nucleon system is studied with a multiconfiguration resonating-group calculation which consists of the dominant configuration d + alpha, the cluster-rearrangement configurations p + He-5 and n + Li-5, and the pseudo-inelastic configuration d* + alpha. The result shows that, because the deuteron cluster is easily distortable, a d + alpha single-configuration study is inadequate. With the addition of the other cluster configurations, the Li-6 ground-state energy is improved by a large amount equal to 1.76 MeV. From an overall viewpoint, the p + He-5 and n + Li-5 configurations are found to contribute more significantly than the d* + alpha configuration, thus confirming the findings from previous seven- and eight-nucleon investigations that single-nucleon transfer processes generally make important contributions and sequential-decay processes are more important than direct-breakup processes in the relatively low-energy region. The d + alpha total reaction cross sections have also been computed and found to agree rather well with empirical results. At 10 MeV, for example, the calculated total reaction cross section is equal to 85% of the empirical value, which is the highest percentage obtained in our six- to eight-nucleon microscopic resonating-group calculations containing no phenomenological imaginary potentials.