If each of X, Y and (X-Y) is a prime number less than 50, how may possible values can X assume?

Claim: For any prime number $X$, there exists a prime number $Y$ such that $X-Y$ is prime if and only if $X-2$ is prime.

Proof. If $X$ is such a prime number, then $X$ is a sum of two prime numbers because $$X=Y+(X-Y).$$ Of course $X$ is odd because $X$ is prime and greater than $2$. So either $Y$ is even or $X-Y$ is even. The only even prime is $2$, so either $Y=2$ or $X-Y=2$. In either case $X-2$ is prime.

Conversely, if $X-2$ is prime then there exists a prime number $Y$ such that $X-Y$ is prime; simply take $Y=2$.

In view of this claim, it suffices to count the number of primes $X<50$ for which $X-2$ is also prime.