We perform a fully correlated study of 6ΛΛHe hypernucleus with two- and three-baryon potentials. We investigate the role of every strength of the strange-sector potentials on the energy breakdown and present a clear understanding of their interplay. The investigation determines the strength of the simulated Nijmegen ΛΛ potential, phenomenologically. We note that the consistency of calculations between 5ΛHe and 6ΛΛHe depends on the ΛN space-exchange strength only, which incidentally determines it. This study is a step forward to pin down all the strengths, to resolve A = 5 anomaly and to search for recently conjectured 4ΛΛH in an authentic way. The study also suggests that the medium effect on strange-sector potentials often written as a repulsive three-body force may be well adapted at two-body level.