(x,y)=(2,8) is a solution to 2y-4x=8, but not the only solution, because you would need two equations for unique values of x and y.
2y=4x=8⇒2y=8, so y=4; and 4x=8⇒x=2, 2y=4x is also true.
So what does (-2,8) mean? It could mean that y=-4x⇒y+4x=0.
Now we could have two equations:
y+4x=0 and 2y-4x=8, from these we would have 3y=8, y=8/3 so 4x=-y=-8/3 and x=-⅔.
Let's check: y+4x=-8/3-8/3=0✔️ 2y-4x=16/3-(-8/3)=16/3+8/3=24/3=8✔️
So the solution would be x=-⅔ and y=2⅔.