1. **Stating the problem:** We have a triangle with a base of length 20 and a horizontal segment inside it parallel to the base with length 8. The vertical sides are divided into segments: left side segments are 10 and 6, right side segments are 6 and 12. We want to find the length marked with an asterisk (*) on the bottom segment near the left side. 2. **Understanding the setup:** The triangle is divided by a segment parallel to the base, creating two smaller triangles similar to the original one. The vertical sides are split into parts, so the triangles formed are similar by AA similarity. 3. **Using similarity ratios:** The ratio of the vertical segments on the left side is $\frac{10}{10+6} = \frac{10}{16} = \frac{5}{8}$. 4. **Applying the ratio to the base:** Since the segment of length 8 is parallel to the base 20, the smaller triangle's base corresponds to the segment 8, and the larger triangle's base is 20. 5. **Finding the length marked with *:** The segment with * is the difference between the smaller base segment and the part corresponding to the vertical segment 6 on the left side. The ratio of the lower vertical segment is $\frac{6}{16} = \frac{3}{8}$. 6. **Calculate the length corresponding to the 6 segment:** Multiply the total base 20 by $\frac{3}{8}$: $$20 \times \frac{3}{8} = \frac{20 \times 3}{8} = \frac{60}{8} = 7.5$$ 7. **Calculate the length marked with *:** The segment with * is the difference between the smaller base segment 8 and 7.5: $$8 - 7.5 = 0.5$$ **Final answer:** The length marked with * is $0.5$ units.