First, let's think about our end goal. The slope-intercept form is y = mx + b. In other words, we want to get y by itself.
Second, let's work with an approach I call "peeling the onion." Since y is the core of the onion, we want to peel away outer layers first and work our way in. We have -3x + 6y on one side of the equation, and our goal is to get "y" by itself, so our outer layer is -3x. To get rid of -3x, we have to do the opposite (for every superhero there's a villain). Opposite - is +, so let's add 3x (+3x) to both sides (gotta keep it balanced!), and we end up with this:
-3x (+ 3x) + 6y = 12 (+ 3x)
6y = 12 + 3x.
Now for our next "layer." 6y is 6 * y, so the opposite of * is /. Let's do that now:
6 (/6) * y = (3x + 12)/6 (notice I rearranged the order. That's perfectly legal)
y = 3/6x + 12/6
Simplify one last time:
y = 1/2x + 2
Hope this helps!!