Vectors in Space · Challenge problem

Vectors $\mathbf a, \mathbf b, \mathbf c, \mathbf d$ in space satisfy $\mathbf a \cdot \mathbf c = 3$, $\mathbf a \cdot \mathbf d = 1$, $\mathbf b \cdot \mathbf c = 2$ and $\mathbf b \cdot \mathbf d = 4$. Find $(\mathbf a \times \mathbf b) \cdot (\mathbf c \times \mathbf d)$.