The equation given in the image is:

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

Let’s solve this step-by-step:

1. First, expand the expression on the left side: $4x - 2(x + 3) = 4x - 2x - 6$

2. Simplify the equation: $4x - 2x - 6 = 8 \implies 2x - 6 = 8$

3. Add 6 to both sides: $2x = 14$

4. Divide both sides by 2: $x = 7$

Thus, the value of $x$ is $7$, corresponding to option $\mathbf{D}$.

Do you want more details on the solving process or have any other questions?

Here are 5 related questions:

1. How would the solution change if the constant term was different, say -2 instead of 8?
2. Can you solve a similar equation: $3x - 4(x - 2) = 5$?
3. How would the solution differ if the equation were $4x + 2(x + 3) = 8$?
4. What is the solution to the equation $5x - 3(x + 1) = 7$?
5. How do you graphically represent the solution of linear equations?

Tip: Always simplify terms and combine like terms before solving for the unknown variable.