So, here is what I did...
Let's start with the original of (y + 6)2 - 8 = 0
Since this is a straightforward quadratic, we can just solve using inverse operations and not worry about expanding the (y+6)2, simplifying and factoring. Plus, once we simplify, we may end up with a trinomial that's not factorable anyways..
Here we go...
Step 1) add 8 to both sides to yield (y+6)2 = 8
Step 2) square root both sides being mindful that when you take the square root of a number, most times you have to take into account BOTH positive and negative values... this then yields y+6 = ±√8
Step 3) subtract 6 on both sides to yield y = -6 ±√8
Step 4) since this question asks us to simplify "as much as possible," we have to simplify ±√8 to ±2√2... If you want clarification on how this is done, please reply and I will walk you through it...
Step 5) box up our final solution of y = -6 ±2√2
Let me know if this helps!! :)