To solve the equation \( \frac{10}{21} = \frac{7}{3}y - \frac{4}{21} \), we can first eliminate the fraction on the left side and combine the fractions on the right.
- Start by adding \(\frac{4}{21}\) to both sides:
\[ \frac{10}{21} + \frac{4}{21} = \frac{7}{3}y \]
- Combine the fractions on the left side:
\[ \frac{10 + 4}{21} = \frac{14}{21} = \frac{2}{3} \]
So now we have:
\[ \frac{2}{3} = \frac{7}{3}y \]
- To isolate \(y\), multiply both sides by \( \frac{3}{7} \):
\[ y = \frac{2}{3} \cdot \frac{3}{7} \]
- Simplifying that gives:
\[ y = \frac{2 \cdot 3}{3 \cdot 7} = \frac{2}{7} \]
Thus, the solution is:
\[ y = \frac{2}{7} \]