1. **Problem statement:** We are given a cuboid with a volume of 3468 mm^3, height of 34 mm, width of 6 mm, and an unknown length. We need to find the length of the cuboid in millimeters. 2. **Formula used:** The volume $V$ of a cuboid is given by the formula: $$V = \text{length} \times \text{width} \times \text{height}$$ 3. **Substitute known values:** $$3468 = \text{length} \times 6 \times 34$$ 4. **Simplify the right side:** $$3468 = \text{length} \times 204$$ 5. **Solve for length:** $$\text{length} = \frac{3468}{204}$$ 6. **Calculate the division:** $$\text{length} = 17$$ 7. **Answer with units:** The length of the cuboid is **17 mm**. This means the missing length dimension is 17 millimeters.