Let's solve the equation step by step to find the value of [tex]\( x \)[/tex]:
We start with the equation:
[tex]\[ 2(3x - 4) = 10x - 8 \][/tex]
First, we distribute the 2 on the left side of the equation:
[tex]\[ 2 \cdot 3x - 2 \cdot 4 = 6x - 8 \][/tex]
So,
[tex]\[ 6x - 8 = 10x - 8 \][/tex]
Next, we move all the [tex]\( x \)[/tex]-terms to one side and the constant terms to the other side. Subtract [tex]\( 6x \)[/tex] from both sides of the equation:
[tex]\[ 6x - 8 - 6x = 10x - 8 - 6x \][/tex]
This simplifies to:
[tex]\[ -8 = 4x - 8 \][/tex]
Now, add 8 to both sides to isolate the [tex]\( x \)[/tex]-term on the right side:
[tex]\[ -8 + 8 = 4x - 8 + 8 \][/tex]
This simplifies to:
[tex]\[ 0 = 4x \][/tex]
Finally, divide both sides of the equation by 4 to solve for [tex]\( x \)[/tex]:
[tex]\[ \frac{0}{4} = x \][/tex]
This simplifies to:
[tex]\[ x = 0 \][/tex]
Hence, the value of [tex]\( x \)[/tex] is [tex]\( \boxed{0} \)[/tex]. Therefore, the correct option is:
[tex]\[ c. \quad 0 \][/tex]
