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:
|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.