If you subtract x from both sides, then you go from
x-2 < x-4
to
-2 < -4
which is a false statement. The value -2 is not smaller than -4. It's the other way around. I recommend looking at a number line to compare the two values.
This means that x-2 < x-4 is never true regardless of what x value you pick. So there are no solutions.