Let's solve the equation step by step:

\[
-g + 2(3 + g) = -4(g + 1)
\]

### Step 1: Distribute the constants
Distribute the \(2\) on the left side, and the \(-4\) on the right side:

\[
-g + 2 \cdot 3 + 2 \cdot g = -4 \cdot g - 4 \cdot 1
\]

Simplify both sides:

\[
-g + 6 + 2g = -4g - 4
\]

### Step 2: Combine like terms
On the left side, combine the terms involving \(g\):

\[
(2g - g) + 6 = -4g - 4
\]

This simplifies to:

\[
g + 6 = -4g - 4
\]

### Step 3: Move the terms involving \(g\) to one side
Add \(4g\) to both sides:

\[
g + 4g + 6 = -4g + 4g - 4
\]

This simplifies to:

\[
5g + 6 = -4
\]

### Step 4: Move the constant term to the other side
Subtract \(6\) from both sides:

\[
5g = -4 - 6
\]

Simplify:

\[
5g = -10
\]

### Step 5: Solve for \(g\)
Divide both sides by 5:

\[
g = \frac{-10}{5} = -2
\]

### Final Answer:
\[
g = -2
\]

Let me know if you'd like further explanation or have any questions!

---

### Here are 5 related questions you can explore:
1. How do you handle equations with more complex terms like fractions or exponents?
2. What are the properties of equality used in solving equations?
3. How do you check if your solution is correct by substituting back into the original equation?
4. How do you solve equations that involve absolute values?
5. What is the difference between solving linear and quadratic equations?

### Tip:
Always simplify each side of the equation step-by-step to avoid mistakes in distributing or combining like terms.

Learn how to solve the linear equation g + 2(3 + g) = -4(g + 1) with a detailed, step-by-step explanation. This solution involves using the distributive property, combining like terms, and applying properties of equality to find the value of g. Suitable for students in Grades 7-9.

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