To solve the equation \( \frac{4}{3} x = -\frac{6}{5} \), we need to isolate \( x \).
We can do this by multiplying both sides of the equation by the reciprocal of \( \frac{4}{3} \), which is \( \frac{3}{4} \).
\[ x = -\frac{6}{5} \cdot \frac{3}{4} \]
Now, multiply the fractions:
\[ x = -\frac{6 \cdot 3}{5 \cdot 4} \] \[ x = -\frac{18}{20} \]
We can simplify \( -\frac{18}{20} \) by dividing both the numerator and the denominator by 2:
\[ x = -\frac{9}{10} \]
So the solution of the equation \( \frac{4}{3} x = -\frac{6}{5} \) is
\[ \boxed{-\frac{9}{10}}. \]