$$\bbox[yellow, 5px, border: 2px solid red] {m\angle \text{ BED} = \dfrac{1}{2}(x^{\circ} + y^{\circ})}$$
$$\bbox[yellow, 5px, border: 2px solid red] {\text{AE} \times \text{EB} = \text{CE} \times \text{ED}}$$
\(m\angle \text{ BED} = \dfrac{1}{2}(84^{\circ} + 30^{\circ})\)
\(m\angle \text{ BED} = \dfrac{1}{2}(114^{\circ})\)
\(m\angle \text{ BED} = 57^{\circ}\)
\(m\angle \text{ BEC} = 180^{\circ}\:-\:57^{\circ}\)
\(m\angle \text{ BEC} = 123^{\circ}\)
\(\text{AE} \times \text{EB} = \text{CE} \times \text{ED}\)
\(8 \times 3 = x\times 6\)
\(24 = 6x\)
\(x = \dfrac{24}{6}\)
\(x = 4\)
