A search was conducted for the 2+2 excitation of the 7.65 MeV, 0+2, Hoyle state in 12C using the 12C(12C, 12C[3α]) 12C reaction. The analysis focussed primarily on the 9.7 MeV region in the 12C excitation energy spectrum and no evidence of a resonance was found. Monte Carlo simulations were used to investigate the minimum strength at which a resonance would need to exist in order to be resolved by the experimental setup used. The possibility was also investigated that the 2+2 resonance may be observed in the 12C(12C, 12C[8Be*+α]) 12C reaction channel, though the methods contained within this thesis allowed only limited analysis of reaction channels involving non-zero spin states in the intermediate 8Be nucleus; no evidence of a resonance was found. Further analysis of the 9.6 MeV and 10 MeV regions of the 12C excitation energy spectrum also revealed no clear sign of a 2+2 resonance.