3x doesn't contian the viarable to solve for. You are going to move it to the right side of the equation by subtracting 3x from both side.
It should look like this: 4y = -3x + 6
Then, mulriply each term by 1/4 and simplify.
Now looks like: 4y/4 = -3x/4 + 6/4
You will cancel your common factors.
You will have: y = -3/4 + 6/4
Reduce by cancelling the common factors.
Factor 2 out of 4
looks like: y = -3x/4 + 2•3/2•2
Cancel your common factors.
Now you have: y = -3x/4 + 3/2
Use your slope intercept y=mx+b
m = -3/4 and b = 3/2
Your slope is -3/4
Your Y-intercept is 3/2