The stability of systems containing six quarks or antiquarks is studied within a simple string model inspired by the strong-coupling regime of quantum chromodynamics and used previously for tetraquarks and pentaquarks. We discuss both six-quark $(q^6)$ and three-quark--three-antiquark $ (q^3\bar q{}^3)$ states. The quarks are assumed to be distinguishable and thus not submitted to antisymmetrization. It is found that the ground state of $(q^6)$ is stable against dissociation into two isolated baryons. For the case of $ (q^3\bar q{}^3)$, our results indicate the existence of a bound state very close to the threshold. The investigations are extended to $(q^3Q^3)$ and $(Q^3\bar q^3)$ systems with two different constituent masses, and their stability is discussed as a function of the mass ratio.