The stronger Goldbach conjecture states that any even integer greater

First of all, this is an interesting fact that I learnt today. Rubina, thanks for posting this!

So, for example, 8 = 5 + 3. We are able to write 8, an even number greater than 7, as a sum of 5 and 3. This is what the conjecture states.

Remember that,
Odd + Odd = Even, Even + Even = Even and Odd + Odd = Even.

126 is an even number. So, the only way that we can get 126 is by adding two different ODD prime numbers.

Also, since we wish to maximize the difference between these two prime numbers, we have to ensure that we make one of them as large as possible and the other as small as possible.

Essentially, this means, one of them needs to be as close as possible to 126 and the other as close as possible to 0 (remember, prime numbers cannot be negative).

The closest prime number (and hence the bigger of the two) to 126 is 113. The other number should therefore be 13. The difference between these two is 100. So, option A can now be eliminated.

We could also take the prime numbers as 109 and 17, but the difference between these two will be 92. Clearly, this is not the largest difference. We can now eliminate options C and hence D & E.

Option B is the correct answer option.

Hope this helps!