To simplify the given expression:

\[
(2x - 3y) - (8x + 6y + 4)
\]

1. Distribute the negative sign through the second parentheses:

\[
= 2x - 3y - 8x - 6y - 4
\]

2. Combine like terms:

\[
= (2x - 8x) + (-3y - 6y) - 4
\]

\[
= -6x - 9y - 4
\]

Thus, the simplified expression is:

\[
-6x - 9y - 4
\]

Would you like a more detailed breakdown of the steps or have any questions? Here are some related questions:

1. How would you simplify the expression \( (4a + 5b) - (2a - 3b + 7) \)?
2. What happens when you have multiple sets of parentheses to simplify?
3. How do you factor the expression \( -6x - 9y - 4 \)?
4. How do you distribute negative signs in algebraic expressions?
5. What are like terms, and why do we combine them?

**Tip:** When distributing a negative sign, be sure to change the signs of all the terms inside the parentheses.

Learn how to simplify the algebraic expression (2x - 3y) - (8x + 6y + 4) by distributing negative signs and combining like terms. This step-by-step solution covers key algebraic concepts such as the distributive property and simplifying expressions. Suitable for students in Grades 6-8.

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