The expression in the image is:

$4y(2xy - 2y^2)$

To simplify this, we can distribute the $4y$ across the terms inside the parentheses:

$4y(2xy) - 4y(2y^2)$

Now, simplify each term:

1. $4y \times 2xy = 8xy^2$
2. $4y \times (-2y^2) = -8y^3$

So, the simplified expression is:

$8xy^2 - 8y^3$

Would you like a more detailed breakdown or have any other questions?

Here are five related questions to consider:

1. What happens if $y = 0$ in the simplified expression?
2. How would you factor this expression $8xy^2 - 8y^3$?
3. What would the expression look like if the variable $x$ had an exponent greater than 1?
4. How does the distributive property help in simplifying expressions like these?
5. What if you added another term inside the parentheses, say $+ 3x^2$?

Tip: When simplifying expressions, always look for common factors that you can factor out to further simplify the result.