To rationalize the denominator of the expression \( \frac{4}{\sqrt{21}} \), we can multiply both the numerator and the denominator by \( \sqrt{21} \):
\[ \frac{4}{\sqrt{21}} \cdot \frac{\sqrt{21}}{\sqrt{21}} = \frac{4\sqrt{21}}{21} \]
Thus, the simplified expression is:
\[ \frac{4\sqrt{21}}{21} \]