Let Diego's age be represented by $D$, and his sister's age by $S$.

From the problem, we have two pieces of information:

1. Diego's sister is twice his age minus 9 years: $S = 2D - 9$

2. Diego's sister is also as old as half the sum of the ages of Diego and his two 12-year-old twin brothers: $S = \frac{1}{2} \left( D + 12 + 12 \right) = \frac{1}{2} (D + 24)$

Now, we can set up the system of equations:

1. $S = 2D - 9$
2. $S = \frac{1}{2} (D + 24)$

To find Diego's age, set these two expressions for $S$ equal to each other:

$2D - 9 = \frac{1}{2} (D + 24)$

This is the equation that can be used to solve for Diego's age $D$.

Do you want me to solve it, or would you like to try it on your own?

Related questions:

1. How old is Diego based on the equation?
2. What would be the equation if his sister were 3 times Diego's age minus 5 years?
3. How would the solution change if the twins were 10 years old instead of 12?
4. What if Diego's sister was only 1 year younger than Diego? How would that affect the equation?
5. Could the system of equations be different if more siblings were involved?

Tip: Always ensure to isolate variables carefully to avoid algebraic mistakes when setting up equations.