Rather than go through all your options, the easiest way to do this is to make a substitution yourself and see if it matches one of the options.
We have:
x+y=6 and x=y+2
We can solve for x on the first one to get x=6-y
Because we have to equations equal to the same thing (x) we can combine them like so:
6-y=y+2
If we rearrange by adding a y to both sides we can see it matches the final choice,
(flipped to match the way they organized it)
y+2+y=6
The final choice is correct.
