To solve the equation \(\frac{5}{6}x = \frac{2}{3}\), you can isolate \(x\) by following these steps:
- Multiply both sides of the equation by the reciprocal of \(\frac{5}{6}\), which is \(\frac{6}{5}\):
\[ x = \frac{2}{3} \cdot \frac{6}{5} \]
- Calculate the right side:
\[ x = \frac{2 \cdot 6}{3 \cdot 5} = \frac{12}{15} \]
- Simplify \(\frac{12}{15}\) by dividing the numerator and the denominator by their greatest common divisor (which is 3):
\[ x = \frac{12 \div 3}{15 \div 3} = \frac{4}{5} \]
Thus, the solution is:
\[ \boxed{\frac{4}{5}} \]