A carbon free radical bears an unpaired electron and is stabilised by electron-releasing alkyl groups through both hyperconjugation and the inductive effect, which help disperse the electron deficiency at the radical centre. A tertiary radical is attached to three alkyl groups, providing the greatest number of hyperconjugative C-H interactions and the strongest electron donation, so it is the most stable of the listed species. A primary radical has only one alkyl group and therefore far less stabilisation, making it less stable. A methyl radical has no alkyl substituents at all and is among the least stable carbon radicals. A vinyl radical sits on an sp^2 carbon adjacent to a double bond, lacks alkyl stabilisation, and is high in energy, so it is not the answer. The ordering tertiary greater than secondary greater than primary mirrors the carbocation trend and is part of the NCERT discussion of reaction intermediates. This stability order also explains why halogenation of alkanes preferentially substitutes at tertiary positions, since the more stable radical forms most readily during the propagation step. Bond dissociation energies confirm the trend, being lowest for the tertiary C-H bond. Plausibility check: greater alkyl substitution always provides more hyperconjugation, so the most substituted, tertiary radical must be the most stable.