1. **State the problem:** We need to find two numbers where the difference between them is 12, and the larger number is twice the smaller number. 2. **Define variables:** Let the smaller number be $x$. 3. **Express the larger number:** Since the larger number is twice the smaller number, the larger number is $2x$. 4. **Write the equation for the difference:** The difference between the larger and smaller number is 12, so: $$2x - x = 12$$ 5. **Simplify the equation:** $$x = 12$$ 6. **Find the larger number:** $$2x = 2 \times 12 = 24$$ 7. **Answer:** The smaller number is $12$ and the larger number is $24$.