1. **State the problem:** Solve for $x$ in the equation $$\frac{x}{12} = \frac{6}{8}$$. 2. **Use the cross-multiplication formula:** For an equation of the form $$\frac{a}{b} = \frac{c}{d}$$, cross-multiply to get $$a \times d = b \times c$$. 3. **Apply cross-multiplication:** $$x \times 8 = 12 \times 6$$ 4. **Simplify the right side:** $$8x = 72$$ 5. **Solve for $x$ by dividing both sides by 8:** $$x = \frac{72}{8}$$ 6. **Show cancellation of common factors:** $$x = \frac{\cancel{72}}{\cancel{8}} = 9$$ 7. **Final answer:** $$x = 9$$ This means the value of $x$ that satisfies the equation is 9.