To solve for \( b \) in the equation
\[ 9 = -\frac{6}{5}b, \]
we'll start by isolating \( b \). First, multiply both sides by \(-\frac{5}{6}\) to get \( b \) by itself:
\[ b = 9 \cdot \left(-\frac{5}{6}\right). \]
Now, compute this multiplication:
\[ b = -\frac{5 \cdot 9}{6} = -\frac{45}{6}. \]
Next, simplify the fraction \(-\frac{45}{6}\):
\[ b = -\frac{15}{2} \quad \text{(after dividing the numerator and denominator by 3)}. \]
Thus, the simplified solution for \( b \) is
\[ b = -\frac{15}{2}. \]