-2x - 8y = 22
-6x -y = 20

You have to eliminate one of the two variables from one equation using the other. For instance, in your given equation ,
-6x-y = 20
can be written as
-y = 20 + 6x
y = -6x - 20
Now we can put this value of y into the first equation
-2x - 8y = 22
putting y = -6x-20
-2x-8(-6x-20)=22
now the equation can be easily solved for x as y has been eliminated.