The question asks for the equation that illustrates the commutative property of addition. This property states that the order of adding numbers does not change the sum. Specifically, for two numbers $a$ and $b$, the commutative property is $a + b = b + a$.

Let’s examine the given options:

a) $2(x - y) = 2x - 2y$ — This is an example of the distributive property, not the commutative property.

b) $12 + (3x + 2) = 9 + 12x + 3x) + 2$ — This expression involves addition, but it doesn’t clearly illustrate the commutative property.

c) $19 + 3m + 8 = 3m + 19 + 8$ — Here, the order of addition changes, which is an example of the commutative property of addition.

d) $4x - 3y = 4x - 3y$ — This expression doesn’t involve any change in the order of addition.

So, the correct choice is c), because it demonstrates how the order of addition can be rearranged: $19 + 3m + 8 = 3m + 19 + 8$.

Would you like a further breakdown or explanation of the properties involved? Here are some related questions you can explore:

1. What is the difference between the commutative property and the associative property of addition?
2. How does the distributive property differ from the commutative property?
3. Can you think of a real-world example where the commutative property of addition is useful?
4. What are the other properties of addition, besides commutative and associative?
5. How can you prove the commutative property using variables or numbers?

Tip: A great way to practice the commutative property is to rearrange the numbers in simple addition problems and verify the result!