To solve the equation \( \frac{4}{3}x = -\frac{6}{5} \), you can follow these steps:
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Isolate \( x \) by multiplying both sides of the equation by the reciprocal of \( \frac{4}{3} \), which is \( \frac{3}{4} \):
\[ x = -\frac{6}{5} \cdot \frac{3}{4} \]
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Multiply the fractions:
\[ x = -\frac{6 \cdot 3}{5 \cdot 4} = -\frac{18}{20} \]
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Simplify the fraction:
\[ x = -\frac{18 \div 2}{20 \div 2} = -\frac{9}{10} \]
So, the solution is:
\[ x = -\frac{9}{10} \]