$S_{ABC} = 8$ $S_{ADC} = S_{ABC} = 8$ $S_{ABCD} = S_{ABC} + S_{ADC} = 16$ $S_{BCD} = S_{ABCD} - S_{ABD}$ $S_{ABD} = S_{ABC} = 8$ $S_{BCD} = 16 - 8 = 8$ $S_{BCD} = \tfrac{1}{2} \times BD \times CH$ $8 = \tfrac{1}{2} \times 6 \times CH$ $8 = 3 \times CH$ $CH = \tfrac{8}{3}$