The problem asks us to simplify the algebraic expression $4b - 3(4 - 2b)$.

1. Problem Description

The problem asks us to simplify the algebraic expression $4b - 3(4 - 2b)$.

2. Solution Steps

First, we distribute the $-3$ across the terms inside the parentheses:

$4b - 3(4 - 2b) = 4b - 3(4) - 3(-2b)$

$4b - 3(4 - 2b) = 4b - 12 + 6b$

Next, we combine like terms. In this case, we combine the $4b$ and $6b$ terms:

$4b - 12 + 6b = (4b + 6b) - 12$

$4b - 12 + 6b = 10b - 12$

3. Final Answer

The simplified expression is $10b - 12$.