1. **State the problem:** We need to find the length of a rectangular prism given its volume and two dimensions: height and width. 2. **Given:** - Volume $V = 42.6$ cubic centimeters - Height $h = 7.5$ cm - Width $w = 2$ cm - Length $l = ?$ 3. **Formula:** The volume of a rectangular prism is given by: $$V = l \times w \times h$$ 4. **Substitute known values:** $$42.6 = l \times 2 \times 7.5$$ 5. **Simplify the right side:** $$42.6 = l \times 15$$ 6. **Solve for $l$ by dividing both sides by 15:** $$l = \frac{42.6}{15}$$ 7. **Show cancellation:** $$l = \frac{\cancel{42.6}}{\cancel{15}} = 2.84$$ 8. **Final answer:** The length of the game piece is $\boxed{2.84}$ cm.