To solve this equation, we first need to simplify each side separately before setting them equal to each other.

Step 1: Simplify the left side of the equation
(х-2) / 5 = (2/3) - ((3х-2) / 6)

Step 2: Solve the equation by first multiplying both sides by 5 to get rid of the denominator on the left side
х - 2 = 5(2/3) - 5((3х-2) / 6)

Step 3: Simplify further
х - 2 = 10/3 - (5/2)(3х - 2)

Step 4: Distribute on the right side of the equation
х - 2 = 10/3 - (15х/2) + 5

Step 5: Combine like terms
х - 2 = 25/3 - 15х/2

Step 6: Multiply through by 6 to get rid of the denominators
6(х - 2) = 6(25/3 - 15х/2)

Step 7: Simplify further
6х - 12 = 50 - 45х

Step 8: Move all the x terms to one side and constant terms to the other side
6х + 45х = 50 + 12

Step 9: Combine like terms
51х = 62

Step 10: Divide by 51 to solve for x
x = 62 / 51

Therefore, x = 62 / 51 or approximately x = 1.22.