Hello,

I suspect you probably mean

|*y*+8| + 2 = 6.

When I use the "vertical bars" (that is, |*y*+8| instead of [*y*+8] with square brackets), I mean the absolute value. If you did not mean this, then ignore what I'm about to write!

When we write |*y*+8|, we mean the absolute value of y+8. Roughly, we mean only "how big"
*y*+8 is, not whether it's positive or negative. For example, |-3| = 3 = |3|; the absolute value of negative 3 is the same as the absolute value of positive 3 (they're both 3).

You also point out that the +4 has a _ sign under the plus, so I suspect what's written on your assignment is really

If |*y*+8| + 2 = 6, then *y*+8 = ±4

(read aloud, you would say, "If the absolute value of the quantity *y*+8, plus 2, equals 6, then
*y*+8 equals plus or minus 4"). That's why the minus sign is under the plus sign, it could be positive or negative 4.

So, I would only partially agree with the answer above. It's still true, but for a different reason. When dealing with absolute values (the vertical lines ||), all we can say is "how big" the number is, not whether it's positive or negative.

Going back to the example I gave, if we were told that |*x|* = 3, then all we could say is
*x* = ±3. That is, *x* = 3 and *x* = -3 are both solutions to the equation |x| = 3. We can only play this game once we get the stuff inside the absolute values by itself. In this case, we can use regular algebra to get there:

If

|y+8| + 2 = 6, then we subtract 2 from both sides to see that

|y+8| = 6 - 2 = 4. Now we have |y+8| = 4, with the absolute value all by itself. Now we can say that

* y*+8 = ±4, so that the statement is true.