1. **State the problem:** Solve the equation $$\frac{x}{15} = \frac{8}{20}$$ for $x$. 2. **Formula and rules:** To solve for $x$ in a proportion, we use cross multiplication: $$a/b = c/d \implies ad = bc$$. 3. **Apply cross multiplication:** $$x \times 20 = 8 \times 15$$ 4. **Calculate the products:** $$20x = 120$$ 5. **Isolate $x$ by dividing both sides by 20:** $$x = \frac{120}{20}$$ 6. **Simplify the fraction:** $$x = \frac{\cancel{120}^{6} \times 20}{\cancel{20}^1} = 6$$ 7. **Final answer:** $$x = 6$$