Let's solve the equation step by step:

Given equation: 

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

### Step 1: Distribute the multiplication on both sides
Distribute the 2 on the left-hand side and the 2 on the right-hand side:

\[
8x - 6 - 8 = 2x + 4
\]

### Step 2: Simplify the equation
Combine like terms on the left-hand side:

\[
8x - 14 = 2x + 4
\]

### Step 3: Move all terms involving \( x \) to one side
Subtract \( 2x \) from both sides:

\[
6x - 14 = 4
\]

### Step 4: Isolate the variable \( x \)
Add 14 to both sides:

\[
6x = 18
\]

Finally, divide by 6:

\[
x = 3
\]

### Solution:
\[
x = 3
\]

Would you like a detailed explanation, or do you have any further questions?

### Related Questions:
1. How would the solution change if the equation were \( 2(4x - 3) - 8 = 3(x + 2) \)?
2. What happens if the constant on the right-hand side is negative?
3. How can you check if your solution to an equation is correct?
4. What is the impact of distributing a negative number instead of a positive number?
5. How do you solve a similar equation with fractions?

**Tip:** Always combine like terms and simplify both sides of the equation before isolating the variable.

Learn how to solve the equation 2(4x - 3) - 8 = 2(x + 2) with a detailed step-by-step solution. This problem involves equations, the distributive property, and solving equations. Suitable for students in Grades 7-9.

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