To divide the fraction \( \frac{6}{7} \) by \( \frac{3}{8} \), you can multiply \( \frac{6}{7} \) by the reciprocal of \( \frac{3}{8} \):
\[ \frac{6}{7} \div \frac{3}{8} = \frac{6}{7} \times \frac{8}{3} \]
Now, multiply the fractions:
\[ \frac{6 \times 8}{7 \times 3} = \frac{48}{21} \]
Next, simplify \( \frac{48}{21} \). Both the numerator and the denominator can be divided by their greatest common divisor, which is 3:
\[ \frac{48 \div 3}{21 \div 3} = \frac{16}{7} \]
So, the result of \( \frac{6}{7} \div \frac{3}{8} \) is:
\[ \frac{16}{7} \]