4x + 12 = -7y
-y + 12 = 4x
solve with elimination

Take the second equation and flip it around so the y on the left ends up on the right and the 4x on the right ends up on the left.  This makes all negatives positive and all positives negative.   -4x   + 12  = y 

Then add the first equation to the second equation 
4x   +12   = -7y
-4x   + 12  = y    this eliminates the x's
          24 = - 6y            then divide by - 6
           - 6     - 6
         - 4    = y

So if you know that y = negative 4, you can substitute into either equation.  I pick the second one because I am a lazy person.  
  -y  + 12  = 4 x
-(-4) + 12 = 4 x     combine your numbers
     16      = 4 x        then divide by 4
       4      =  x
So your solution is: x = 4 and y = -4 or this is also written (4, -4)

Does that work for you?