To solve the equation 9x - 14/9 = -2/3, we need to isolate the variable x.

First, let's get rid of the fractions by multiplying every term in the equation by the least common denominator (LCD), which is 9.

9(9x) - 9(14/9) = 9(-2/3)

81x - 14 = -6

Next, let's isolate the x term by adding 14 to both sides of the equation.

81x - 14 + 14 = -6 + 14

81x = 8

Finally, divide both sides of the equation by 81 to solve for x.

81x/81 = 8/81

x = 8/81

Therefore, the solution to the equation 9x - 14/9 = -2/3 is x = 8/81.