A study of the 1 2 C( 2 4 Mg, 1 2 C 1 2 C) 1 2 C reaction has revealed discrete states at excitation energies between 20 and 30 MeV in 2 4 Mg. Angular correlation analyses of some of the lower energy states confirms the report by earlier authors of monotonically increasing spin values consistent with a rotational sequence. Comparison with breakup observed in the 1 2 C( 2 0 Ne, 1 2 C 1 2 C) 8 Be reaction suggests that the same states in 2 4 Mg are populated, while the difference in laboratory cross sections in the two reactions is interpreted as evidence for the association of the breakup states with a prolate hyper-deformed configuration appearing in theoretical calculations for 2 4 Mg.