When you have an equation with just x and y terms, you're looking at a straight line.
One way to approach is it, as you say, to add -5 to both sides, and then divide across by 2, so that the LHS just contains y on its own. Then you have it in the form y = mx + c, and you can just read off the y-intercept as c.
Another way to find the y-intercept is to set x=0, and see what you're left with:
2y+0 = -6
So the point (0,-3) is on the line, and is the y-intercept.
You also want to graph it. Since it's a straight line, you just need two points, then draw the line with a ruler.
Let's get the x-intercept as our other point:
So (-6/5,0) is tyhe x-intercept, and the second point we need for drawing the line.
Oops, typo. In case you're confused, I meant "One way to approach it is, as you say, to add -5x to both sides..."