Final answer:
The two spinocerebellar tracts responsible for carrying proprioceptive input to the cerebellum are the dorsal spinocerebellar tract and the ventral spinocerebellar tract.
Step-by-step explanation:
The spinocerebellar tracts carry unconscious proprioceptive input from muscle spindles and Golgi tendon organs (GTOs) to the cerebellum for the coordination of movement. The names of the two main spinocerebellar tracts are the dorsal spinocerebellar tract and the ventral spinocerebellar tract. The dorsal tract carries proprioceptive information from the lower body and legs, while the ventral tract carries similar information but can also convey signals from the upper parts of the body.