Solve the equation \( \frac{6}{7} - x = \frac{1}{3} \) and verify the solution.

Let's solve the equation \( \frac{6}{7} - x = \frac{1}{3} \):
1. Isolate \( x \):
\[ x = \frac{6}{7} - \frac{1}{3} \]
2. Find a common denominator for \( \frac{6}{7} \) and \( \frac{1}{3} \):
The least common denominator of 7 and 3 is 21.
\[ \frac{6}{7} = \frac{18}{21}, \quad \frac{1}{3} = \frac{7}{21} \]
3. Subtract the fractions:
\[ x = \frac{18}{21} - \frac{7}{21} = \frac{11}{21} \]
4. Verify the solution by substituting \( x = \frac{11}{21} \) back into the original equation:
\[ \frac{6}{7} - \frac{11}{21} = \frac{18}{21} - \frac{11}{21} = \frac{7}{21} = \frac{1}{3} \]
The solution is correct.

**Answer:** \( x = \frac{11}{21} \).