To divide fractions, you multiply the first fraction by the reciprocal of the second fraction.
So, for \(-\frac{3}{4}\) divided by \(\frac{3}{8}\):
\[ -\frac{3}{4} \div \frac{3}{8} = -\frac{3}{4} \times \frac{8}{3} \]
Now, multiply the numerators and the denominators:
\[ -\frac{3 \times 8}{4 \times 3} = -\frac{24}{12} \]
Now simplify \(-\frac{24}{12}\):
\[ -\frac{24}{12} = -2 \]
Thus, \(-\frac{3}{4} \div \frac{3}{8} = -2\).