Can i generate a SHA512 hash if i know the SHA256 hash of some unknown data? if the SHA256 Hash of some unknown data is known !
Can i find the SHA512 of that unknown data ?
No, you can’t.

There are (at most) $2^{256}$ different possible SHA-256 hashes.

If it were possible to deduce a SHA-512 hash from a SHA-256 hash with no knowledge of the data, then there would be at most as many different SHA-512 hashes as different SHA-256 hashes.

Then, a SHA-512 hash would be at most as strong as a 256-bit hash.