1. **State the problem:** Calculate the value of $16 \left( \frac{8.68}{0.29} \right)^2$. 2. **Formula and rules:** We need to first divide $8.68$ by $0.29$, then square the result, and finally multiply by $16$. 3. **Calculate the division:** $$\frac{8.68}{0.29} = 29.93103448275862 \approx 29.93$$ 4. **Square the result:** $$29.93^2 = 29.93 \times 29.93 = 895.8049$$ 5. **Multiply by 16:** $$16 \times 895.8049 = 14332.8784$$ 6. **Final answer:** $$16 \left( \frac{8.68}{0.29} \right)^2 \approx 14332.88$$