The expression provided in the image is:

$4x - 2(4y - x) - 7y$

Let's simplify this step by step:

1. Distribute the $-2$ across the parentheses: [ 4x - 2(4y - x) = 4x - [2 \times 4y] + [2 \times x] = 4x - 8y + 2x ]

2. Combine like terms: $4x + 2x - 8y - 7y = 6x - 15y$

So, the simplified expression is:

$6x - 15y$

Would you like more details on any of the steps, or do you have any specific questions?

Here are five related questions to deepen your understanding:

1. How can the distributive property be applied in more complex algebraic expressions?
2. Can you factor the simplified expression $6x - 15y$?
3. What happens if the expression is set equal to zero? How would you solve for $x$ or $y$?
4. How would this expression change if $4y - x$ were replaced with $x + y$?
5. How can you apply this method to expressions involving higher powers of $x$ and $y$?

Tip: Always perform the distribution carefully, watching out for signs, especially when negative values are involved.