Question: User: $\frac{2}{3}r=4$
1. **State the problem:** Solve the equation $$\frac{2}{3}r = 4$$ for the variable $r$.
2. **Formula and rules:** To isolate $r$, multiply both sides of the equation by the reciprocal of $\frac{2}{3}$, which is $\frac{3}{2}$.
3. **Intermediate work:**
$$\frac{3}{2} \times \frac{2}{3} r = \frac{3}{2} \times 4$$
4. **Simplify the left side:**
$$\cancel{\frac{3}{2}} \times \cancel{\frac{2}{3}} r = 6$$
5. **Result:**
$$r = 6$$
**Explanation:** Multiplying both sides by $\frac{3}{2}$ cancels the fraction on the left, leaving $r$ alone. Then multiplying $4$ by $\frac{3}{2}$ gives $6$.