The book says the answer is -4x+y=12 but my answer was 3y=7x-9how did they get that answer

So first, you want to distribute the 7/3 to both the x and -3 inside the parenthesis. After this you get:

y - 4 = 7/3x - 7

Then move the 7/3 to the other side, and the -4 to the other, by using the opposite operations.

y - 7/3x = -7 + 4

And then:

y - 7/3x = -3

Then to make everything an integer, multiply by 3.

3y - 7x = -9

It could also be 3y = 7x - 9.

So it seems to me that your answer was correct. The answer key could just be incorrect, as it is in many cases, you could be looking at the wrong question's answer, etc.