I'm playing in a game where the following rule states:

Adjacent characters can attack each other; they do so with 6 vs 8 modified dice.

What does this exactly mean? Is this the same as a modified border?

-- I don't know which game you are talking about, but most likely the answer is "yes", it's essentially a modified border.  If you are not sure, check it in the "board explorer". 

Regardless, as you initiate an attack, the dice/border mods show up in the attack dialog box so you can confirm.