The post-selection technique was proposed by Christandl, König, and Renner [Phys. Rev. Lett. 102, 020504 (2009)] to simplify the security of quantum-key-distribution schemes. This work applies this technique to derive the security bounds for the six-state Scarani-Acin-Rigbordy-Gisin 2004 quantum key distribution protocol. This protocol can extract secure keys from a source emitting multi-photons due to its robustness from photon number splitting attacks, making it a good candidate for practical implementations. We also compare the security bounds for this protocol under collective attacks to the security bounds obtained after applying the post-selection technique when using finite resources. Our results demonstrate that the bounds for optimal attack are close to the bound for collective attack for many signals. Notably, the six-state SARG04 protocol proves to be more robust to the PNS attacks when compared to the original four-state SARG04 protocol. This demonstrates the power of the post-selection technique in deriving the security bounds for the six-state protocol when finite resources are used.