To multiply the fractions \( \frac{4}{5} \) and \( \frac{1}{3} \), you multiply the numerators together and the denominators together:
\[ \frac{4}{5} \times \frac{1}{3} = \frac{4 \times 1}{5 \times 3} = \frac{4}{15} \]
So, \( \frac{4}{5} \times \frac{1}{3} = \frac{4}{15} \).
Thus, the answer is:
\[ \frac{4}{15} \]
In your format, it would be written as \([4]/[15]\).