$\sqrt[3]{-8\times 12y^3}$

Key concept: To simplify this expression, factor out the perfect cube inside the radical first, then simplify the variable part.

Step by step

Step 1: Separate the perfect cube factor

$\sqrt[3]{-8\times 12y^3} = \sqrt[3]{-8}\,\sqrt[3]{12y^3}$

Since $-8 = (-2)^3$, we have

$\sqrt[3]{-8} = -2$

Also,

$\sqrt[3]{y^3}=y$

Step 2: Simplify the remaining factor

$\sqrt[3]{12y^3} = y\sqrt[3]{12}$

So the expression becomes

$-2y\sqrt[3]{12}$

Final answer

$\boxed{-2y\sqrt[3]{12}}$

Pitfall alert

Do not combine $-8\times 12$ into $-96$ and then try to guess the cube root mentally unless you are checking for a perfect cube. It is safer to pull out the obvious cube factor $-8$ first.

Try different conditions

If the expression were $\sqrt[3]{-8\times 12y^6}$, then $y^6$ would contribute $y^2$ outside the radical, giving $-2y^2\sqrt[3]{12}$.

Further reading

cube root, factorization, radical expression