A complete set of analyzing powers (AP`s), {ital iT}{sub 11}, {ital T}{sub 20}, {ital T}{sub 21}, and {ital T}{sub 22}, for 50 MeV {sup 12}C({sup 6}Li(vector),{sup 6}Li) elastic scattering and inelastic scattering to the {sup 12}C(2{sup +}, 4.44 MeV), {sup 12}C(0{sup +}, 7.65 MeV), and {sup 12}C(3{sup {minus}}, 9.64 MeV) states over the center-of-mass (c.m.) angular range 10{degree}{endash}115{degree} is reported. In addition, cross sections for the excited states 3{sup +}(2.18 MeV), 2{sup +}(4.31 MeV), and 1{sup +}(5.65 MeV) of {sup 6}Li were measured by using the inverse-kinematics reaction {sup 6}Li({sup 12}C,{sup 12}C) at 100 MeV. A combined analysis of the new 50 MeV data and previous 30 MeV data has been carried out using the coupled-channels (CC) code FRESCO. The CC calculations use an optical potential with double-folded (DF) real central, Woods-Saxon imaginary central, and Thomas real spin-orbit (SO) potentials. Calculations include reorientation terms and coupling to the first three excited states of {sup 6}Li and the first two nonzerospin states of {sup 12}C. The {sup 6}Li coupling strengths were fixed by the measured {sup 6}Li excited-state cross sections. The elastic-scattering cross sections and A.P.`s are described well. The need for an explicit SO potential is apparent in the elasticmore » and inelastic-scattering AP`s {ital iT}{sub 11}, more so at 30 MeV than at 50 MeV. The rank-2 AP`s up to 50{degree} c.m. arise mainly from ground-state reorientation effects. The DF potential normalization constant {ital N} approaches unity for the 50 MeV data. At both energies, the {sup 12}C(2{sup +}) cross sections are underestimated at large angles, and the description of the {sup 12}C(3{sup {minus}}) cross sections is poor in detail. The {sup 12}C(3{sup {minus}}) AP`s and the {sup 12}C(2{sup +}) {ital iT}{sub 11} are not reproduced at either energy. {copyright} {ital 1996 The American Physical Society.}« less