Smallest Positive Integer which is Sum of 2 Odd Primes in 6 Ways

Theorem
The smallest positive integer which is the sum of $2$ odd primes in $6$ different ways is $60$.

Proof
It is determined that there are no smaller numbers with this property by inspection:

From the workings of Smallest Positive Integer which is Sum of 2 Odd Primes in n Ways, $48$ is the smallest positive integer which is the sum of $2$ odd primes in $5$ different ways.

Thus there is no need to explore smaller numbers.