Let's solve the inequality:

### Given:
\[
8 + 4(-f - 6) \leq 4f - 6 - 2f
\]

### Step 1: Distribute the \(4\) on the left-hand side:
\[
8 + 4(-f - 6) = 8 - 4f - 24 = -4f - 16
\]

So the inequality becomes:
\[
-4f - 16 \leq 4f - 6 - 2f
\]

### Step 2: Simplify the right-hand side:
\[
4f - 6 - 2f = 2f - 6
\]

Now the inequality is:
\[
-4f - 16 \leq 2f - 6
\]

### Step 3: Move the terms involving \(f\) to one side and the constant terms to the other:
\[
-4f - 2f \leq -6 + 16
\]
\[
-6f \leq 10
\]

### Step 4: Solve for \(f\):
Divide both sides by \(-6\). Remember that when dividing by a negative number, the inequality sign flips:
\[
f \geq \frac{10}{-6}
\]
\[
f \geq -\frac{5}{3}
\]

### Final Answer:
\[
f \geq -\frac{5}{3}
\]

Would you like further details or have any questions?

Here are 5 related questions for further practice:
1. Solve: \(3f - 7 \geq 2f + 5\)
2. Solve: \(2(f - 3) \leq f + 6\)
3. Solve: \(5f + 8 < 3f - 2\)
4. Solve: \(4f - 12 > 3f + 7\)
5. Solve: \(6 - 2f \leq 10f - 18\)

**Tip**: Always remember to flip the inequality sign when multiplying or dividing both sides by a negative number.

Learn how to solve the linear inequality 8 + 4(−f−6) ≤ 4f − 6 − 2f with a detailed, step-by-step explanation. This problem involves core algebraic concepts, such as the distributive property and solving inequalities by flipping the sign when dividing by negative numbers. Suitable for students in Grades 8-10.

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