Clearly, 6 votes are not enough: for example, if you get one vote in each region, there will be six ties and nobody will get elected. With 7 votes for your party there are several ways how these can be distributed. We can easily check that in each of them you are sure to win the elections.
For example, you can get both votes in two of the regions and a single vote in three other regions. In that case, you won in two regions, and you forced a tie in three other regions, leaving at most one region for some other party.