To solve the equation \( \frac{4}{7} - x = \frac{1}{3} \), we can follow these steps:

1. Start by isolating \( x \):

\[
\frac{4}{7} - x = \frac{1}{3}
\]

2. Rearrange the equation to solve for \( x \):

\[
-x = \frac{1}{3} - \frac{4}{7}
\]

3. To combine the fractions on the right, we need a common denominator. The least common multiple of 3 and 7 is 21. Thus, we rewrite the fractions:

\[
\frac{1}{3} = \frac{7}{21} \quad \text{and} \quad \frac{4}{7} = \frac{12}{21}
\]

4. Substituting these into the equation gives us:

\[
-x = \frac{7}{21} - \frac{12}{21}
\]

5. Now, simplify the right side:

\[
-x = \frac{7 - 12}{21} = \frac{-5}{21}
\]

6. To solve for \( x \), we multiply by -1:

\[
x = \frac{5}{21}
\]

So, the solution is:

\[
x = \frac{5}{21}
\]