Public Key Cryptography: Diffie-Hellman Key Exchange
Alice didn't know that $16\equiv 3^{24}\mod 17$. The video just made it clearer that they were intrisically computing the same value.

I'm guessing that the point the video was trying to make was that 
$$3^{54\times24}\equiv3^{24\times54}\equiv 16^{54}\equiv15^{24}\equiv1\mod 17.$$