Let's rewrite the expression \( 6(d - 6f) - 6f - 3(-7f + 8d) \) step by step:

1. **Distribute** the constants inside the parentheses:
   \[
   6(d - 6f) = 6d - 36f
   \]
   \[
   -3(-7f + 8d) = 21f - 24d
   \]

2. Now substitute these into the original expression:
   \[
   (6d - 36f) - 6f + (21f - 24d)
   \]

3. **Combine like terms**:
   - For \(d\)-terms: \(6d - 24d = -18d\)
   - For \(f\)-terms: \(-36f - 6f + 21f = -21f\)

4. So the simplified expression is:
   \[
   -18d - 21f
   \]

The fully simplified form is \( \boxed{-18d - 21f} \).

Would you like further details on any of the steps?

Here are 5 related questions you can explore:
1. How do you simplify expressions with multiple variables?
2. What are the rules for distributing negative numbers in algebra?
3. Can you factor out common terms from the simplified expression?
4. How do like terms help in simplifying expressions?
5. How do parentheses affect operations in an algebraic expression?

**Tip:** Always remember to carefully distribute signs when simplifying expressions, especially when negatives are involved!

This guide explains how to simplify the algebraic expression 6(d - 6f) - 6f - 3(-7f + 8d). It covers key algebra concepts, such as the distributive property and combining like terms. The solution is ideal for students in Grades 7-9, helping them practice basic algebraic manipulations.

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