Goldbach twin and cousin primes

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Good day.

My question is a counterexample for the following: Is every even number greater than 4 the sum of a number that belongs to set the cousin primes with another number that belongs to the set of twin primes?

Cousin primes (p,q) in the sense that if p is prime, then p+4 is other prime number.

I verify it up 1000. For example, and curiously, for 556=239+317 no there are much goldbach partitions that solve the question.