  We find four kinds of six-parameter family of coupled Painlev\'e VI systems
in dimension four with affine Weyl group symmetry of types $B_6^{(1)}$,
$D_6^{(1)}$ and $D_7^{(2)}$. Each system is the first example which gave
higher-order Painlev\'e equations of types $B_l^{(1)},D_l^{(1)}$ and
$D_l^{(2)}$, respectively. Each system can be expressed as a polynomial
Hamiltonian system. We show that these systems are equivalent by an explicit
birational and symplectic transformation, respectively. By giving each
holomorphy condition, we can recover each system. These symmetries, holomorphy
conditions and invariant divisors are new. We also give an explicit description
of a confluence process from the system of type $D_6^{(1)}$ to the system of
type $A_5^{(1)}$ by taking the coupling confluence process from the Painlev\'e
VI system to the Painlev\'e V system.
