You can always add or subtract same value to/from both sides of equation. The same is true about multiplication and division.
In your case you have to subtract x from both sides of equation in order to get rid of it on the left side:
[tex]x+2y-x=8-x[/tex]
[tex]2y=8-x[/tex]
But it's easier to remember that if you want to move some member of equation to other side, you just have to change it's sign. Let's practice a bit using your equation (I have added "plus" signs where they are usually omitted to better understend what's going on):
[tex]+x+2y=+8[/tex]
Move 2y to the right side:
[tex]+x=+8-2y[/tex]
Move 8 to the left side:
[tex]+x+2y-8=0[/tex]
Move both x and 2y to the right side:
[tex]0=8-x-2y[/tex]
