1. The problem is to solve for $r$ in the equation $$\frac{3}{5} r = 2.$$\n\n2. To isolate $r$, divide both sides of the equation by $\frac{3}{5}$. The formula used is $$r = \frac{2}{\frac{3}{5}}.$$\n\n3. Dividing by a fraction is the same as multiplying by its reciprocal, so \n$$r = 2 \times \frac{5}{3}.$$\n\n4. Multiply the numerators and denominators: $$r = \frac{2 \times 5}{3} = \frac{10}{3}.$$\n\n5. Therefore, the solution is $$r = \frac{10}{3}.$$\n\n6. To confirm, substitute $r = \frac{10}{3}$ back into the original equation: $$\frac{3}{5} \times \frac{10}{3} = \frac{3 \times 10}{5 \times 3} = \frac{30}{15} = 2,$$ which is true.