y = -4x - 8      (1)
-8x + 4y = -8    (2)

You just have y expressed via x in equation (1).
So, simply substitute it into equation (2). You will get a single equation for x:

-8*x + 4*(-4x - 8) = -8.

Simplify and solve it:

-8x - 16x - 32 = -8,

-24x = -8 + 32,
-24x = 24,

x =  = -1.

Now from (1) y = -4x - 8 = -4*(-1) - 8 = 4 -8 = -4.

Answer. x = -1, y = -4.

You didn't show your work, or reveal your answers. 

For that reason, I won't show mine either but I'll tell you this much:  

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