Let's solve the expression in the problem:

We are given: $2x - 4y - 10x + 8y$

To simplify, combine like terms:

1. Combine the $x$-terms: $2x - 10x = -8x$

2. Combine the $y$-terms: $-4y + 8y = 4y$

So, the simplified expression is: $-8x + 4y$

Now, let's check the options provided:

• A. $-4xy$ — Incorrect, not in the same form as the simplified expression.
• B. $8x - 12y$ — Incorrect, wrong coefficients.
• C. $-8x + 4y$ — Correct, this matches the simplified expression.
• D. $-12x - 12y$ — Incorrect, wrong coefficients.

The correct answer is C.

Would you like further details or have any questions?

Here are 5 related questions:

1. How do you combine like terms in an algebraic expression?
2. What are the steps to factor a polynomial expression?
3. How do you solve an equation with multiple variables?
4. What is the difference between like terms and unlike terms?
5. How would you simplify expressions involving parentheses?

Tip: Always group and combine like terms carefully to avoid mistakes in simplification!