This is an easy one:

(1) [y+14] = -y-14

or

(2) [y+14] = y+14

Doing the math, we have for (1) is -12 and (2) is -16, therefore, -12-16 = -28

Given that 22 - |y + 14| = 20 and we need to find the the sum of all possible values of y

To open |y + 14| we need to take two cases (Watch this video to know about the Basics of Absolute Value)

Case 1: Assume that whatever is inside the Absolute Value/Modulus is non-negative

=> y + 14 ≥ 0 => y ≥ -14

|y + 14| = y + 14 (as if A ≥ 0 then |A| = A)
=> 22 - (y + 14) = 20
=> 22 - y -14 = 20
=> 8 - 20 = y
=> y = -12
And our condition was y ≥ -14. Definitely -12 ≥ -14
=> y = -12 is a solution

Case 2: Assume that whatever is inside the Absolute Value/Modulus is Negative

y + 14 < 0 => y < -14

|y + 14| = -(y + 14) (as if A < 0 then |A| = -A)
=> 22 - (-(y + 14)) = 20
=> 22 + y + 14 = 20
=> y = 20 - 36
=> y = -16
And our condition was y < -14. Definitely -16 < -14
=> x = -16 is a solution

=> Sum of all possible values of y = -12 + (-16) = -12 -16 = -28

So, Answer will be A
Hope it helps!

Watch the following video to learn How to Solve Absolute Value Problems