1. **Problem statement:** We have two circles, circle C with radius 8 units and circle D with radius 10 units. The centers C and D are 14 units apart. The circles intersect at points F and H, and points E, C, F, H, D, and G lie on the same horizontal line. We need to find the length of segment HD. 2. **Understanding the problem:** Since the circles intersect, the points F and H are the intersection points. The line through E, C, F, H, D, and G is horizontal, so points C, H, and D lie on the same line. We know the distance CD = 14 units. 3. **Key insight:** The segment HD is part of the line CD. Since C and D are centers of the circles, and H is an intersection point, the distances CH and HD relate to the radii of the circles. 4. **Using the radii:** The radius of circle C is 8 units, so the distance from C to H is 8 units: $CH = 8$. The radius of circle D is 10 units, so the distance from D to H is $HD$ (unknown). 5. **Using the total length:** Since points C, H, and D are collinear and $CD = 14$, we have: $$CH + HD = CD$$ $$8 + HD = 14$$ 6. **Solving for HD:** $$HD = 14 - 8 = 6$$ 7. **Answer:** The length of HD is 6 units. **Final answer:** $\boxed{6}$ units.