The problem asks us to find the slope $m$ and y-intercept $b$ of the line given by the equation $3x - 2y = 12$.

1. Problem Description

The problem asks us to find the slope $m$ and y-intercept $b$ of the line given by the equation $3x - 2y = 12$.

2. Solution Steps

First, we need to rewrite the equation in slope-intercept form, which is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

We start with the given equation:

$3x - 2y = 12$

Subtract $3x$ from both sides:

$-2y = -3x + 12$

Divide both sides by $-2$:

$y = \frac{-3x}{-2} + \frac{12}{-2}$

$y = \frac{3}{2}x - 6$

Now, we can identify the slope and y-intercept. The slope $m$ is the coefficient of $x$, and the y-intercept $b$ is the constant term.

Therefore, $m = \frac{3}{2}$ and $b = -6$.

3. Final Answer

The slope $m$ and y-intercept $b$ of the line are $m = \frac{3}{2}$ and $b = -6$.

So the answer is D. $m = \frac{3}{2}, b = -6$.