To solve this equation, we first need to distribute the 1 1/3 (which is 4/3) to the expression inside the parentheses:

4/3 * (1/3 - x) = 8/27

Next, we multiply 4/3 by 1/3 and by -x:

4/9 - 4/3x = 8/27

Now, we need to combine the constants on one side and the terms with x on the other side:

4/9 = 8/27 + 4/3x

To simplify, we need to find a common denominator for 27 and 3, which is 27:

4/9 = 8/27 + 36/27x
4/9 = 8/27 + 36x/27

Now, we can combine the fractions:

4/9 = (8 + 36x)/27

To solve for x, we can cross multiply:

4 27 = 9 (8 + 36x)
108 = 72 + 324x

Subtract 72 from both sides:

36 = 324x

Divide by 324:

36/324 = x

x = 1/9

Therefore, the solution to the equation is x = 1/9.