Let's solve the equation step-by-step:

We start with:

$3x + 8 = x - 4(x - 2)$

Step 1: Expand the expression on the right-hand side

Distribute $-4$ to both terms inside the parentheses:

$3x + 8 = x - 4x + 8$

Step 2: Combine like terms on the right-hand side

Simplify the terms involving $x$:

$3x + 8 = -3x + 8$

Step 3: Move all terms involving $x$ to one side

Add $3x$ to both sides to get all the $x$-terms on one side:

$3x + 3x + 8 = 8$

Simplify:

$6x + 8 = 8$

Step 4: Move constant terms to the other side

Subtract $8$ from both sides:

$6x = 0$

Step 5: Solve for $x$

Divide both sides by 6:

$x = 0$

Final Answer:

$x = 0$

Would you like a more detailed explanation of any part?

Here are 5 follow-up questions:

1. How do we solve equations with parentheses?
2. What happens if there are fractions in an equation like this?
3. How do you handle variables on both sides of the equation?
4. Can equations with no solution or infinite solutions look similar to this?
5. How would you solve an equation involving exponents or powers?

Tip: When distributing terms or simplifying, always make sure to keep track of signs to avoid small errors that can affect your final answer!