Which value of x satisfies the equation \( \frac{5}{4}\left(x-\frac{2}{3}\right)=\frac{20}{3} \) ?

To solve the equation \( \frac{5}{4}\left(x-\frac{2}{3}\right)=\frac{20}{3} \), we first eliminate the fraction by multiplying both sides by 4: \[ 5\left(x-\frac{2}{3}\right) = \frac{80}{3} \] Next, we divide both sides by 5: \[ x - \frac{2}{3} = \frac{80}{15} \] This simplifies to: \[ x - \frac{2}{3} = \frac{16}{3} \] Now, add \(\frac{2}{3}\) to both sides: \[ x = \frac{16}{3} + \frac{2}{3} \] This combines to: \[ x = \frac{18}{3} = 6 \] Thus, the value of \( x \) that satisfies the equation is \( \boxed{6} \).