Sorry, that's wrong. Do it this way:

 First equation:   8x - 6y =  4
Second equation:   2x -  y = -2

Solve the second equation for y, that's because y in the
second equation has a coefficient of -1 and that makes 
it solvable without fractions:

Second equation:   2x -  y = -2
                        -y = -2 - 2x

Consider the coefficient of y to be -1

                       -1y = -2 - 2x

Then divide through by -1

                        =  - 

                         y = 2 + 2x


Since y and 2 + 2x are equal you can sustitute (2 + 2x) in place of y in
the first equation:

 First equation:   8x - 6y = 4
                   8x - 6(2 + 2x) = 4
Solve that for x:  
                    8x - 12 - 12x = 4 
                         -4x - 12 = 4
                              -4x = 16
                                x = 
                                x = -4

Go back to where you solved for y

                                y = 2 + 2x

and since x and -4 are equal you can substitute (-4) for x
and find y:

                               y = 2 + 2x
                               y = 2 + 2(-4)
                               y = 2 - 8
                               y = -6

So the solution is x = -4, y = -6, often written as (x,y) = (-4,-6)

Edwin