how do I change 2y-3x=6 into slope y intercept form explain....?

2y - 3x = 6 Add 3x to both sides.
2y = 3x + 6 Divide by 2
y = 3x/2 + 6/2
y = 1.5x + 3

2y=3x+6

y=(3/2)x+x

To put it in slope-intercept form, solve for y.

y = mx + b ------ slope intercept form, you can see that y is alone at the left side of the equation

solve for y
2y-3x=6
add 3x to both sides
2y - 3x + 3x = 6 + 3x
2y = 6 + 3x ------ y is now alone at the left side, but it has a coefficient of 2
divide both sides by 2
2y/2 = (6 + 3x)/2
y = 6/2 + 3/2x
y = 3 + 3/2x
arrange the terms at the right side
y = 3/2x + 3

How the heck did you ever get this far in math without knowing how to manipulate a simple equation?

y-int let x equal to zero
hence
2y-3(0)=6
2y=6
y=6/2
y=3