A Fraction Coefficient

The equation $\frac{2}{3}x = 8$ says that two thirds of a number is 8. The coefficient of $x$ is the fraction $\frac{2}{3}$. To undo a coefficient, you divide both sides by it. Dividing by $\frac{2}{3}$ is the same as multiplying by its reciprocal, $\frac{3}{2}$, because $\frac{\frac{2}{3}\cdot 3}{2} = 1$. So multiply both sides by $\frac{3}{2}$:

$$\frac{\frac{3}{2}\cdot 2}{3}x = \frac{3}{2}\cdot 8$$

$$x = 12$$

Multiplying by the reciprocal turned the coefficient into 1 and left $x$ on its own. Check the answer: two thirds of 12 is 8.

You can also do this in two smaller steps. Multiply both sides by 3 to get $2x = 24$, then divide both sides by 2 to get $x = 12$. Both ways give the same answer. In both, you are done when the coefficient in front of $x$ is 1.