Correct option is A.
It produces 4 beats/s with a fork of frequency $510 \mathrm{~Hz}$.
Hence its frequency can be 514 or $506 \mathrm{~Hz}$. It also produces 6 beats/s with a fork of frequency $512 \mathrm{~Hz}$. Hence its frequency can be $518 \mathrm{~Hz}$ or $506 \mathrm{~Hz}$.
Hence the frequency $506 \mathrm{~Hz}$ is possible in both cases.