My grandmother and Hank's great grandmother were sisters. What are Hank and I to each other?

You and Hank's parent (whichever is in the blood line) are the children of first cousins, so you are second cousins.

Hank is one generation removed from this relationship, so you are second cousins once removed. Confusingly, it's expressed the same from both ends, i.e. he is your second cousin once removed, and you are his second cousin once removed also.

The rule is to take the 'straight across' relationship of the senior of the two people involved (in this case you and Hank's parent being second cousins) and 'remove' down from that as many generations as necessary to reach the junior person (Hank). If you're still confused, believe me you are not alone!

There's an excellent post with examples of all this just down the page.

Thanks, Ewood. That was very helpful, as is the link you provided.