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$\mathbf{a}, \mathbf{b}, \mathbf{c}, \mathbf{d}$ are coplanar vectors, then $(\mathbf{a} \times \mathbf{b}) \times(\mathbf{c} \times \mathbf{d})$ is equal to
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$0$
We have, $\mathbf{a}, \mathbf{b}, \mathbf{c}$ and $\mathbf{d}$ are coplanar vectors, then $\mathbf{a} \times \mathbf{b}$ and $\mathbf{c} \times \mathbf{d}$ are perpendicular on the same plane, therefore, $\mathbf{a} \times \mathbf{b}$ and $\mathbf{c} \times \mathbf{d}$ both are parallel to each other, then $(\mathbf{a} \times \mathbf{b}) \times(\mathbf{c} \times \mathbf{d})=0$
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