Which one of the following encryption methodologies allows you to maintain the privacy of an email communication, and ensure the origin of the message using PGP?

Sharing your private key with anyone destroys the entire trust model of asymmetric cryptography, as your private key must remain secret at all times.

Encrypting first with your private key creates a digital signature that proves origin, since only you possess your private key. Encrypting again with the destination's public key ensures only the intended recipient - who holds the matching private key - can decrypt and read the message, achieving both authentication and confidentiality as designed in the PGP standard.

You do not have access to the destination's private key; encrypting with the destination's private key would mean anyone with the destination's public key could decrypt it, providing no confidentiality.

Encrypting with the destination's private key is impossible in practice since you never possess another party's private key, and this approach would provide no origin authentication.