The additive identity property states that when any number is added to 0, the result is always the number itself. In other words, 0 acts as the additive identity because it does not change the value of any number when added to it.

Let's examine each option to determine which one represents the additive identity property of 0:

a) 1 + 0 = 20
In this case, adding 0 to 1 should result in 1 itself. However, the equation given states that the sum is 20, which is incorrect. Therefore, option 'a' does not represent the additive identity property of 0.

b) 29 + 18 = 18 + 29
This equation does not involve 0, so it does not represent the additive identity property. It simply shows that addition is commutative, meaning the order of the numbers does not change the sum. Therefore, option 'b' is not the correct answer.

c) 14 + 0 = 14
This equation perfectly demonstrates the additive identity property. When 0 is added to 14, the sum is still 14. This aligns with the definition of the additive identity property. Therefore, option 'c' represents the additive identity property of 0 and is the correct answer.

d) (2 + 3) + 4 = 2 + (3 + 4)
This equation is an example of the associative property of addition, which states that the grouping of numbers being added does not affect the sum. It does not involve 0, so it does not represent the additive identity property. Therefore, option 'd' is not the correct answer.

In summary, option 'c' (14 + 0 = 14) represents the additive identity property of 0 because the sum remains the same when 0 is added to 14.