1. **Problem Statement:** We have triangle ABC with points D, E, and F on its sides. Given that AE = EC and BF = FC, points E and F are midpoints of sides AC and BC respectively. We know EF = 8 and DF = 10. We need to find the length AB. 2. **Key Observations:** Since E and F are midpoints, segment EF is a mid-segment of triangle ABC, parallel to side AB and half its length. This is a property of mid-segments in triangles. 3. **Formula Used:** The Mid-segment Theorem states: $$EF = \frac{1}{2} AB$$ 4. **Applying the theorem:** Given EF = 8, $$8 = \frac{1}{2} AB \implies AB = 2 \times 8 = 16$$ 5. **About DF:** The length DF = 10 is given but not necessary to find AB in this problem since EF and the midpoint conditions suffice. 6. **Final Answer:** $$\boxed{16}$$ Thus, the length of side AB is 16.