Under this plan, the county executive ---much like a president or governor - would propose a budget and the county council - much like a state legislature or the congress - would pass it or change it. If the executive doesn't like the changes, he can veto them line by line. The council in turn could over-ride the veto.
It's customary for legislatures and the congress to need a 2/3 majority to override a veto, but the requirement is slightly greater in what's under consideration here. With an 11-member council, a two-thirds majority would be 7.3. So the writers of Issue 6 decided to round-up and require 8 votes to over-ride; they could just as easily rounded down and made it only seven. In other words, they could have made it slightly harder for the executive's will to prevail but instead made it slightly easier.