Let's simplify the expression $2a(6 - 9a)$.

To do this, we distribute the $2a$ to each term inside the parentheses:

$2a \times 6 - 2a \times 9a$

This results in:

$12a - 18a^2$

So, the simplified expression is:

$12a - 18a^2$

Let me know if you'd like further details or have any questions!

Here are some related questions for further exploration:

1. How would the expression change if we had a negative sign in front of the parentheses, like $-2a(6 - 9a)$?
2. What is the value of this expression when $a = 3$?
3. How can we factor $12a - 18a^2$ completely?
4. How would we solve for $a$ if $12a - 18a^2 = 0$?
5. What is the difference between distributing terms and factoring an expression?

Tip: Always double-check the signs when distributing to avoid errors!