Given $x>0$, simplify $\sqrt[3]{8 x^{24}}$ completely.

Step 1 ：Given the expression \(\sqrt[3]{8 x^{24}}\).

Step 2 ：The expression is a cube root. To simplify it, we need to find the cube root of the constant and the cube root of the variable part separately.

Step 3 ：The cube root of 8 is 2.

Step 4 ：The cube root of \(x^{24}\) is \(x^{8}\) because \(\frac{24}{3} = 8\).

Step 5 ：So, the simplified form of the given expression is \(2x^{8}\).

Step 6 ：Final Answer: \(\boxed{2x^{8}}\)