Well, if you try to find the coordinate of (3,4), you'll find that it'll in the positive plane in the 3rd quadrant.
When you have an equation 4x + 3y= 12, it means that you'll multiply 4 by 1, 2, 3...etc., then add three onto it.
Ex: 4x + 2y = 8
Why is 4x + 2y = 8? Think of the "x" as the "times 1". So, like I said it's multiplying 1, 2, 3, etc.
Your equation would look like this if you wanted to see the process:
Ex: 4 x 1 + 2 x 1 = 8
4 x 2 + 2 x 2 = 10
But for some, it's just more confusing. So the simplified version is easier to understand. To answer your question, an equation that'll be parallel to
4x + 3y =12, is -4x + -3y = 12
