1. **State the problem:** We are given two triangles ABC and ECD with AB parallel to ED, and lines ACD and BCE are straight. We know the lengths AB = 8 cm, AC = 4.8 cm, BC = 6.4 cm, and ED = 20 cm. We need to find the length of BE. 2. **Identify the relationship:** Since AB is parallel to ED and ACD and BCE are straight lines, triangles ABC and ECD are similar by the AA similarity criterion (corresponding angles are equal). 3. **Use the similarity ratio:** The ratio of corresponding sides between triangles ECD and ABC is $$\frac{ED}{AB} = \frac{20}{8} = 2.5$$. 4. **Calculate lengths in triangle ECD:** Using the similarity ratio, lengths corresponding to AC and BC in triangle ECD are scaled by 2.5. 5. **Calculate BE:** Since BE corresponds to BC scaled by 2.5, we have $$BE = 2.5 \times BC = 2.5 \times 6.4 = 16$$ cm. **Final answer:** The length of BE is 16 cm.