1. **State the problem:** We need to find a page number between 10 and 20 whose two digits add up to 6. 2. **Understand the problem:** The page number is a two-digit number, so it can be written as $10a + b$ where $a$ is the tens digit and $b$ is the units digit. 3. **Set up the equation:** The sum of the digits is given as $a + b = 6$. 4. **List possible values:** Since the book has 20 pages, $a$ can be 1 (for pages 10 to 19) or 2 (for page 20). 5. **Check for $a=1$:** $$1 + b = 6 \implies b = 5$$ So the page number is $10 \times 1 + 5 = 15$. 6. **Check for $a=2$:** $$2 + b = 6 \implies b = 4$$ So the page number is $10 \times 2 + 4 = 24$, but the book only has 20 pages, so this is invalid. 7. **Conclusion:** The page number is $15$. **Final answer:** The page number is **15**.