Sure, let's solve the equation step-by-step. We're given the equation:
[tex]\[ 4 - 2(b - 6) = 12 \][/tex]
First, let's simplify the expression inside the parentheses and distribute the \(-2\):
[tex]\[ 4 - 2(b - 6) = 4 - 2b + 12 \][/tex]
Next, let's combine like terms on the left side:
[tex]\[ 4 + 12 - 2b = 16 - 2b \][/tex]
So, the equation becomes:
[tex]\[ 16 - 2b = 12 \][/tex]
Now, let's isolate the term with the variable by subtracting 16 from both sides:
[tex]\[ 16 - 2b - 16 = 12 - 16 \][/tex]
This simplifies to:
[tex]\[ -2b = -4 \][/tex]
Now, divide both sides by \(-2\) to solve for \(b\):
[tex]\[ b = \frac{-4}{-2} = 2 \][/tex]
So, the correct solution is [tex]\(\boxed{2}\)[/tex].
