Answer:
(-2, -2)
Explanation:
Compare the two functions ...
f(x) = -|x +2| -2
f(x) = a·g(x -h) +k
where f(x) is a translation and scaling of function g(x). Here, you have ...
g(x) = |x|
The scale factor is a = -1.
The horizontal shift is h = -2.
The vertical shift is k = -2.
_____
The original vertex at (0, 0) has been shifted by (h, k) to ...
(0, 0) + (h, k) = (0, 0) + (-2, -2) = (-2, -2).