1. **State the problem:** Solve the equation $$\frac{2j}{5} = 6$$ for the variable $j$. 2. **Formula and rules:** To solve for $j$, we need to isolate it on one side of the equation. Since $j$ is multiplied by $\frac{2}{5}$, we can multiply both sides by the reciprocal of $\frac{2}{5}$, which is $\frac{5}{2}$. 3. **Multiply both sides by $\frac{5}{2}$:** $$\frac{5}{2} \times \frac{2j}{5} = 6 \times \frac{5}{2}$$ 4. **Simplify the left side by canceling common factors:** $$\cancel{\frac{5}{2}} \times \frac{2j}{\cancel{5}} = 6 \times \frac{5}{2}$$ $$j = 6 \times \frac{5}{2}$$ 5. **Calculate the right side:** $$j = \frac{6 \times 5}{2} = \frac{30}{2} = 15$$ 6. **Final answer:** $$j = 15$$ This means the value of $j$ that satisfies the equation is 15.