The given equation is:

$6y - 3x = -12$

Let's solve for $y$ in terms of $x$.

Step 1: Isolate the term with $y$

To do this, move $-3x$ to the right side of the equation:

$6y = 3x - 12$

Step 2: Solve for $y$

Now, divide everything by 6 to solve for $y$:

$y = \frac{3x - 12}{6}$

Step 3: Simplify

We can simplify the fraction:

$y = \frac{3x}{6} - \frac{12}{6}$

This simplifies to:

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

So the equation in slope-intercept form is:

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

This is the final equation for $y$ in terms of $x$.

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Do you want further details, or do you have any questions?

Here are some related questions to explore:

1. What is the slope of the line $y = \frac{x}{2} - 2$?
2. How would the graph of this equation look like?
3. What is the $y$-intercept of the line?
4. How would you solve for $x$ if $y = 4$?
5. Can you rewrite the equation in standard form?

Tip: To graph a linear equation, start by identifying the slope and the $y$-intercept.