Within the framework of SU(3) flavor symmetry, we investigate two-body doubly charmful baryonic B -> B-c(B) over bar (c)' decays, where B-c(B) over bar (c)' represents the anti-triplet charmed dibaryon. We determine the SU(3)(f) amplitudes and calculate B(B- -> Xi(0)(c) Xi(-)(c)) = (3.4(-0.9)(+1.0)) x 10(-5) and B((B) over bar (0)(s) -> Lambda(+)(c) Xi(c)+) = (3.9(-1.0)(+1.2)) x 10(-5) induced by the single W-emission configuration. We find that the W-exchange amplitude, previously neglected in studies, needs to be taken into account. It can cause a destructive interfering effect with the W-emission amplitude, alleviating the significant discrepancy between the theoretical estimation and experimental data for B((B) over bar (0) -> Lambda(+)(c) Lambda(-)(c)). To test other interfering decay channels, we calculate B((B) over bar (0)(s) -> Xi(0(+))(c) (Xi) over bar (0(+))) = (3.0(-1.1)(+1.4)) x10(-4) and B((B) over bar (0) -> Xi(0)(c)(Xi) over bar (0)(c)) = (1.5(-0.6)(+0.7)) x10(-5). We estimate non-zero branching fractions for the pure W-exchange decay channels, specifically B((B) over bar (0)(s) ->Lambda(+)(c) Lambda(-)(c)) = (8.1(-1.5)(+1.7))x10(-5) and B((B) over bar (0) -> Xi(+)(c)(Xi) over bar (-)(c)) = (3.0 +/- 0.6)x10(-6). Additionally, we predict B(B-c(+) -> Xi(+)(c)(Xi) over bar (0)(c)) = (2.8(-0.7)(+0.9)) x10(-4) and B(B-c(+) -> Lambda(+)(c)(Xi) over bar (0)(c)) = (1.6(-0.4)(+0.5)) x10(-5), which are accessible to experimental facilities such as LHCb.