1. **Problem:** Solve the proportion $$\frac{3}{8} = \frac{15}{x}$$ 2. **Formula:** Cross multiply to solve proportions: $$a/b = c/d \implies ad = bc$$ 3. **Step 1:** Cross multiply: $$3 \times x = 8 \times 15$$ 4. **Step 2:** Simplify: $$3x = 120$$ 5. **Step 3:** Divide both sides by 3 to isolate $x$: $$\frac{\cancel{3}x}{\cancel{3}} = \frac{120}{3}$$ 6. **Step 4:** Simplify division: $$x = 40$$ 7. **Answer:** The solution to the proportion is $$x = 40$$.