To solve the equation \( \frac{x}{3} = \frac{2}{3} + \left( -\frac{1}{7} \right) \), we need to perform the following steps:

1. Simplify the right-hand side of the equation.
2. Solve for \( x \).

Let's start by simplifying the right-hand side:

\[ \frac{2}{3} + \left( -\frac{1}{7} \right) = \frac{2}{3} - \frac{1}{7} \]

To subtract these fractions, we need a common denominator. The least common denominator (LCD) of 3 and 7 is 21. We convert each fraction to have this common denominator:

\[ \frac{2}{3} = \frac{2 \times 7}{3 \times 7} = \frac{14}{21} \]
\[ -\frac{1}{7} = -\frac{1 \times 3}{7 \times 3} = -\frac{3}{21} \]

Now we can subtract the fractions:

\[ \frac{14}{21} - \frac{3}{21} = \frac{14 - 3}{21} = \frac{11}{21} \]

So the equation now is:

\[ \frac{x}{3} = \frac{11}{21} \]

To solve for \( x \), we multiply both sides of the equation by 3:

\[ x = 3 \times \frac{11}{21} \]

Simplify the right-hand side:

\[ x = \frac{3 \times 11}{21} = \frac{33}{21} \]

We can simplify this fraction by dividing the numerator and the denominator by their greatest common divisor, which is 3:

\[ x = \frac{33 \div 3}{21 \div 3} = \frac{11}{7} \]

So the solution to the equation is:

\[ x = \frac{11}{7} \]