1. **State the problem:** We have a triangle ABC with a smaller segment DE parallel to AB inside it. Given lengths are DE = 6, BE = 4, BC = 8, and AB = x. We want to find the value of $x$ using similar triangles. 2. **Identify similar triangles:** Since DE is parallel to AB, triangle CDE is similar to triangle CBA by the AA (Angle-Angle) similarity criterion. 3. **Write the similarity ratio:** Corresponding sides of similar triangles are proportional. So, $$\frac{DE}{AB} = \frac{CE}{CB}$$ 4. **Express CE in terms of BC and BE:** Since $BE = 4$ and $BC = 8$, then $$CE = BC - BE = 8 - 4 = 4$$ 5. **Substitute known values into the ratio:** $$\frac{6}{x} = \frac{4}{8}$$ 6. **Simplify the right side:** $$\frac{4}{8} = \frac{1}{2}$$ 7. **Set up the equation:** $$\frac{6}{x} = \frac{1}{2}$$ 8. **Cross multiply:** $$6 \times 2 = 1 \times x$$ $$12 = x$$ 9. **Final answer:** $$x = 12$$ This means the length of side AB is 12.