We report on double and single differential cross section measurements of the 1s2s(2) S-2, 1s2s2p P-2 +/-, and 1s2s2p P-4 doubly excited states produced by single-electron capture in 6-15 MeV collisions of pre-excited C4+(1s2s S-3) ions with H-2, He, Ne, and Ar targets. Ab initio cross section calculations based on a three active electrons atomic orbital close-coupling approach are compared to the measurements for collisions with the lighter H-2 and He targets, showing an overall good agreement. Theoretical details concerning Auger electron angular distributions, partial cross sections, impact parameter dependencies, and radiative cascade feeding effects are discussed. The populations of the 1s2s2p P-4, P-2_, P-2(+) multiplets concerning the spin symmetry are finally presented for the four collision systems and discussed following the comparisons between theory and experiment.