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