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We find four kinds of six-parameter family of coupled Painlev\'e VI systemsin 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 gavehigher-order Painlev\'e equations of types $B_l^{(1)},D_l^{(1)}$ and$D_l^{(2)}$, respectively. Each system can be expressed as a polynomialHamiltonian system. We show that these systems are equivalent by an explicitbirational and symplectic transformation, respectively. By giving eachholomorphy condition, we can recover each system. These symmetries, holomorphyconditions and invariant divisors are new. We also give an explicit descriptionof a confluence process from the system of type $D_6^{(1)}$ to the system oftype $A_5^{(1)}$ by taking the coupling confluence process from the Painlev\'eVI system to the Painlev\'e V system.

Coupled Painlev\'e VI systems in dimension four with affine Weyl group symmetry of types $B_6^{(1)}$, $D_6^{(1)}$ and $D_7^{(2)}$