1. **State the problem:** Calculate the value of $12 \sqrt{8.64}$.\n\n2. **Recall the formula:** The square root of a number $x$ is a value $y$ such that $y^2 = x$.\n\n3. **Calculate the square root:** $\sqrt{8.64} = 2.94$ because $2.94^2 = 8.64$.\n\n4. **Multiply by 12:** $12 \times 2.94 = 35.28$.\n\n**Final answer:** $12 \sqrt{8.64} = 35.28$.