The 12C+12C fusion reaction was studied in the range of Ec.m.=8.9 MeV to 21 MeV using the active-target Time Projection Chamber. With the full information of all the tracks of the reaction products, the cross section of the 12C(12C,8Be)16Ogs channel and the 12C(12C,3α)12C channel have been measured down to the level of a few milibarns. The 12C(12C,8Be)16Ogs reaction channel is determined to be 10-8
+24 mb at Ec.m.=11.1 MeV, supporting the direct α transfer reaction mechanism. The 12C(12C,3α)12C reaction channel was studied for the first time using the exclusive measurement. Our result does not confirm the anomaly behavior reported in the previous inclusive measurement. Our comparisons with the statistical model calculations suggest that the 3α channel is dominated by the fusion evaporation process at Ec.m.>19 MeV. The additional contribution of the 3α channel increases the fusion reaction cross section by 10% at energies above 20 MeV. We also find that additional reaction mechanism is needed to explain the measured cross section at Ec.m.< 15 MeV where the statistical model prediction vanishes.