If y is negative shouldn't it be x+2y = 6?
The basic idea is that a variable can represent a negative value, and if it does, then any subtraction or addition in an equation is therefore reversed, in a way.
Say, for example, that y = -1
In the expression x - y, then, we are NOT looking at x - 1. Instead, we have x - (-1), which is x + 1. Even though we are subtracting y (as in x - y), we are increasing the value (as in x + 1).
Similarly, in x - 2y, we would have x + 2.
So in the equation x + |y| - y, we are increasing the value twice: once with "+ |y|" and once with "- y".
So to simplify that, we subtract 2y from x, because y is negative, so we're actually increasing the value.
In case this still isn't clear, let's break it down as much as possible and compare the two equations using y = -1:
x + |y| - y = 6
x + |y| - (y) = 6
x + |-1| - (-1) = 6
x + 1 - (-1) = 6
x + 1 + 1 = 6
x + 2 = 6
Now let's compare this result with the equation x - 2y = 6,
x - 2y = 6
x - (2 * -1) = 6
x - (-2) = 6
x + 2 = 6
See how we start with a negative and end up with the same result?