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Explanation:

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∠DAC = ∠DBC [angle subtended in same segment by same chord are equal]
Similarly,
∠ADB = ∠ACB
∠CDB = ∠CAB
∠ACD = ∠ABD

∆AED is similar to ∆BEC
[∠DAC = ∠DBC and ∠ADB = ∠ACB]
∴ $\frac{\mathrm{ED}}{\mathrm{EC}}$ = $\frac{\mathrm{AD}}{\mathrm{BC}}$ = $\frac{4}{5}$   ...(1)

∆AEB is similar to ∆DEC
[∠CDB = ∠CAB and ∠ACD = ∠ABD]
∴ $\frac{\mathrm{AE}}{\mathrm{ED}}$ = $\frac{\mathrm{AB}}{\mathrm{CD}}$ = $\frac{2}{1}$   ...(2)

(1) × (2)
⇒$\frac{\mathrm{ED}}{\mathrm{EC}}\times \frac{\mathrm{AE}}{\mathrm{ED}}$ = $\frac{4}{5}\times \frac{2}{1}$ = $\frac{8}{5}$

Hence, option (d).