By definition, a prime number is a positive integer, excluding '1', that is divisible only by itself and '1'.
For purpose of explanation, allow me to paraphrase the question as:
"Consider m and n being prime numbers. How many ways can the sum of m and n be equal to 24."
The answer to this question can be derived systematically as follows by listing m (all prime numbers<24 or until it repeats in column for n), then the possibility of n being prime:
"m", "possible n", "is n a prime number?"
2, 22, no
3, 21, no
5, 19, yes
7, 17, yes
11, 13, yes
Any value of m beyond 11 would have been repeated as n previously.
Hence my answer to this question is:
There are exactly 3 ways of expressing 24 as the sum of two prime numbers.