To solve this equation for x, we can start by applying the inverse cosine function to both sides:

cos(x/3-П/6) = sqrt(2)/2

arccos(cos(x/3-П/6)) = arccos(sqrt(2)/2)

x/3 - П/6 = ±?/4

Now we can solve for x by multiplying both sides by 3 and adding ?/2:

x = (±3?/4 + ?/2) + П

Simplifying this expression, we get:

x = (3?/4 + П/2) + П or x = (-3?/4 + П/2) + П

Therefore, the solutions for x are:

x = (5?/4 + П) or x = (?/4 + П)