  Within the framework of $SU(3)$ flavor symmetry, we investigate two-body
doubly charmful baryonic $B\to{\bf B}_c\bar{\bf B}'_c$ decays, where ${\bf
B}_c\bar{\bf B}'_c$ represents the anti-triplet charmed dibaryon. We determine
the $SU(3)_f$ amplitudes and calculate ${\cal B}(B^-\to \Xi_c^0\bar
\Xi_c^-)=(3.4^{+1.0}_{-0.9})\times 10^{-5}$ and ${\cal B}(\bar B^0_s\to
\Lambda_c^+\bar \Xi_c^-)=(3.9^{+1.2}_{-1.0})\times 10^{-5}$ 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 ${\cal B}(\bar B^0\to\Lambda_c^+\bar\Lambda_c^-)$. To test other
interfering decay channels, we calculate ${\cal B}(\bar B^0_s\to
\Xi_c^{0(+)}\bar \Xi_c^{0(+)})=(3.0^{+1.4}_{-1.1})\times 10^{-4}$ and ${\cal
B}(\bar B^0\to \Xi_c^0\bar \Xi_c^0)=(1.5^{+0.7}_{-0.6})\times 10^{-5}$. We
estimate non-zero branching fractions for the pure $W$-exchange decay channels,
specifically ${\cal B}(\bar B^0_s\to \Lambda_c^+\bar
\Lambda_c^-)=(8.1^{+1.7}_{-1.5})\times 10^{-5}$ and ${\cal B}(\bar B^0\to
\Xi_c^+\bar \Xi_c^-)=(3.0\pm 0.6)\times 10^{-6}$. Additionally, we predict
${\cal B}(B^+_c\to \Xi_c^+\bar \Xi_c^0)=(2.8^{+0.9}_{-0.7})\times 10^{-4}$ and
${\cal B}(B^+_c\to \Lambda_c^+\bar \Xi_c^0)=(1.6^{+0.5}_{-0.4})\times 10^{-5}$,
which are accessible to experimental facilities such as LHCb.
