To find the value of [tex]\( x \)[/tex] that makes the equation [tex]\( 2(x + 8) = x + 20 \)[/tex] true, we can solve the equation step-by-step.
1. Distribute the 2 on the left-hand side:
[tex]\[
2(x + 8) = x + 20
\][/tex]
This becomes:
[tex]\[
2x + 16 = x + 20
\][/tex]
2. Move all terms involving [tex]\( x \)[/tex] to one side of the equation. Subtract [tex]\( x \)[/tex] from both sides:
[tex]\[
2x + 16 - x = x + 20 - x
\][/tex]
Simplifying this, we get:
[tex]\[
x + 16 = 20
\][/tex]
3. Isolate [tex]\( x \)[/tex] by subtracting 16 from both sides:
[tex]\[
x + 16 - 16 = 20 - 16
\][/tex]
Simplifying this, we find:
[tex]\[
x = 4
\][/tex]
Thus, the value of [tex]\( x \)[/tex] that makes the equation [tex]\( 2(x + 8) = x + 20 \)[/tex] true is [tex]\( \boxed{4} \)[/tex]. Therefore, the correct option is:
D. 4
