when you check second equation; y is isolated then we will plug in y in the first equation
but there is 8y in the second equation not -16y;
when you multiply 8 by -2 you get -16; so you need to multiply second equation bu -2 first
-2(8y = 6 +2x) gives us -16y = -12 -4x as you see both equations have -16y;
you can plug that -16y = -12 -4x in to the first equation.
when you see -16y in the first equation just plug -12 -4x since they are equal to each other.
first equation 4x-16y=18 becomes 4x -12 -4x = 18
you get -12 = 18 it is impossible furthermore there is no solution.
Hope that helps