Let's define the unknown number as $x$.

The problem states two expressions:

1. "Six times a number" is $6x$.
2. "Nine more than two times the number" is $2x + 9$.

The difference between these two expressions is: $6x - (2x + 9)$ Now, distribute the negative sign: $6x - 2x - 9 = 4x - 9$

So, the difference is $4x - 9$.

Would you like further clarification or details?

Here are five related questions:

1. How do you solve for $x$ when you have a specific equation involving this expression?
2. What if the number was negative? How would it change the difference?
3. Can you set the difference equal to a value and solve for $x$?
4. How do we apply distributive property when simplifying such expressions?
5. How does this translate to a word problem in a real-world context?

Tip: Always distribute the negative sign carefully when subtracting algebraic expressions to avoid common errors.