A digital signature has to prove two things at once: that the message has not been altered, and that it really came from the claimed sender. The mechanism therefore combines two operations.

First the message is put through a cryptographic hash function to produce a short fixed-length digest. Any change to the message, however small, changes the digest, which is what secures integrity.

Then the sender encrypts that digest with their own private key. Because only the sender holds that key, anyone can decrypt the digest with the sender's public key and, on finding it matches a freshly computed hash of the message, is assured of the sender's identity and of non-repudiation.

The other options fail one of the two tests. Symmetric key encryption alone uses a shared key, so either party could have produced the message and identity cannot be proved. Plaintext compression only shortens data. Salting of passwords defends stored password hashes against precomputed attacks and has nothing to do with signing a message.

Hence, the answer is hashing with private key signing.