Private key encryption is often used in conjunction with public key encryption. However, a secret is required to be known by both party.
Commonly, this method is used after a secret is computed by applying the public key encryption. Assuming that a private key is available, each party can use the private key to both encrypt and decrypt.
The purpose of private key encryption is that it is fast. However, it also suffers from easier exposure. So, if a private key needs to be computed and shared between two parties, public key encryption is used first as it is much harder to break.