To divide the fraction \( \frac{3}{4} \) by \( \frac{1}{8} \), we can use the rule for dividing fractions, which is to multiply the first fraction by the reciprocal of the second fraction.
The reciprocal of \( \frac{1}{8} \) is \( \frac{8}{1} \).
So, we have:
\[ \frac{3}{4} \div \frac{1}{8} = \frac{3}{4} \times \frac{8}{1} \]
Now, we can multiply the fractions:
\[ \frac{3 \times 8}{4 \times 1} = \frac{24}{4} \]
Next, we simplify \( \frac{24}{4} \):
\[ \frac{24}{4} = 6 \]
Therefore, \( \frac{3}{4} \div \frac{1}{8} = 6 \).
So the final answer is:
\[ 6 \]