  The exotic state $X(5568)$ which was observed by D0 Collaboration is very
likely to be a tetraquark state with four different valence quark flavors,
though the existence was not confirmed by other collaborations. The possibility
of such state still generate lots of interests in theory. In the paper, we will
study the properties of the state under the SU(3) flavor symmetry. This four
quark state with a heavy bottom quark and three light quarks(anti-quark) can
form a $6$ or $\overline {15}$ representation. The weak decays can be dominant
and should be discussed carefully while such state is stable against the strong
interaction. Therefor we will study the multi-body semileptonic and nonleptonic
weak decays systematically. With the help of SU(3) flavor symmetry, we can give
the Hamiltonian in the hadronic level, then obtain the parameterized
irreducible amplitudes and the relations of different channels. At the end of
the article, we collect some Cabibbo allowed two-body and three-body weak decay
channels which can be used to reconstruct $X_{b6}$ states at the branching
fraction up to be $10^{-5}$.
