You can solve it this way:
First, make first equation simple by dividing it by 2
6x+2y=8
3x+y=4
Then, multiply it by -3
-9x-3y=-12
Now you've got the second equation
-9x+ky=-11
if k=-3
-9x-3y=-12
-9x-3y=-11
6x+2y=8
2y=-6x+8
y=-3x+4
-9x+ky=-11
ky=9x-11
y=(9/k)x-(11/k)
(9/k)=-3
9=-3k
k=9/(-3)
k=-3
