Math Help - Basketball game problem

Sorry for the lame title, couldn't thinnk of a better one xD
Anyways, can anyone please tell me how to solve this problem:

At a basketball tournament involving 8 teams, each team played 4 games with each of the other teams. How many games were played at this tournament?

The mark scheme says: since each team 4 games with other teams, 8*4= 32 games are played by each team. each game involved two teams, hence 32*(8/2)=128 games were played.

hmmm, so, if each team plays 4 games with each other team, but not itself (which is rediculous) , shouldn't it be 4*7=28 games each team, also, why do we divide the number of teams by two? I know it says there is two teams each match, but what effect why do we divide it by two?
Please help me, I am just confused, I just need a good explanation to remove this confusion.....

Originally Posted by IBstudent
At a basketball tournament involving 8 teams, each team played 4 games with each of the other teams. How many games were played at this tournament?
I am a bit concerned about the wording used in this question. I am woefully ignorant of sports. A tournament in which each team plays each other team four times seems a bit much. But let’s say that is correct.
It can be modeled as an multi-graph on eight vertices in which there are four edges between any two vertices.
$\binom{8}{2}=28$, so there are 28 pairing of teams.
Four edges, games, for each pair: $112$.