To find the quotient when dividing \(-\frac{3}{4}\) by \(\frac{3}{8}\), you can use the rule that dividing by a fraction is the same as multiplying by its reciprocal.
First, let's rewrite the division as multiplication by the reciprocal:
\[ -\frac{3}{4} \div \frac{3}{8} = -\frac{3}{4} \times \frac{8}{3} \]
Now multiply the fractions:
\[ -\frac{3 \times 8}{4 \times 3} = -\frac{24}{12} \]
Now simplify \(-\frac{24}{12}\):
\[ -\frac{24}{12} = -2 \]
Thus, the quotient when you divide \(-\frac{3}{4}\) by \(\frac{3}{8}\) is \(-2\).
So the answer is \(-2\).