The technique of reflection high energy electron diffraction (RHEED) has been applied to study the evolution of various superstructures on 6H-SiC (0001) as a function of annealing temperature. Between the evolution of the stable 3x3 and √3x√3R30 o phases on a silicon-enriched 6H-SiC (0001), a mixed phase 3x3/2x2 reconstruction followed by a well-defined 6x6 reconstruction was observed by RHEED for the first time. The 6x6 reconstruction is distinct from the pseudo-periodic 6x6 structure suggested previously for graphite moire pattern on 6H-SiC (0001) [Surf. Sci. 48 (1975) 463; Surf. Sci. 256 (1991) 354].The mechanisms for the formation of these superstructures in the sequence of 3x3,6x6,√3x√3R30 o and 6√3x6√3R30 o between 800 o C to 1200 o C were discussed. The 6x6 structure is proposed to evolve directly from the 3x3 following the missing of consecutive Si clusters in the twisted silicon adlayer model. Annealing the 6x6 reconstructed surface to 1000 o C gives rise to a √3x√3R30 o reconstruction. From here, the segregation of carbon domains occurs readily and these form an incommensurate 6√3x6√3R30 epilayer at 1200 o C. At the early stages of the annealing, the 6√3x6√3R30 RHEED pattern consists of a series of cluster satellite streaks superimposed on 1x1 SiC. Further annealing results in the appearance of graphite streaks with its basis vectors rotated 30 o to SiC. Prolonged annealing of the graphitized surface results in the growth of single crystalline graphite multilayers on the 6H-SiC substrate.