Answer:
-2pi/3
Step-by-step explanation:
y = 2 cos 3(x + 2π∕3) +1
y = A sin(B(x + C)) + D
amplitude is A
period is 2π/B
phase shift is C (positive is to the left)
vertical shift is D
We have a shift to the left of 2 pi /3
So first, you get the absolute value to one side:

Next, set up two equations; One where the value inside the absolute value lines is positive, and another where it is negative, and solve both for the variable:

Your answers are
8 and -8, or +-8.