Total points Team F got was

The given table is

For any team, a win fetches 2 points, a draw fetches 1 point, and a loss fetches no points.

Team A scored 8 points and it played 5 matches.

So the only possibility is that A won 3 matches and 2 were draws. (3*2+2*1 = 8)

In all other cases, A will never score 8 points.

Similarly, for B it can score 6 points from 3 matches only when it has won all three matches, as B has lost 2 matches.

For C, the score is 5 points, and it lost 2 matches. It can be achieved if C wins 2 matches and draws 1 match.

The score for D is 5 points, and it lost 1 match, so it can be achieved if D wins 1 match and draws 3 matches.

Filling the table with wins and draws.

Now, it is given that both teams E and F ended with less than 5 points.

Team E has lost 1 match, if it had won 1 match and drawn the remaining 3 matches, the score would be 2*1+3*1 = 5

But, it has scored less than 5 points.

So, E has not won a match; all 4 matches were drawn and he obtained a total score of 4.

When six teams are playing and each team plays 1 match against another team, there will be $$^6C_2=15$$ matches.

Each match will result in two points to the winning team or, if it draws, 1 point to each team.

The sum of points of all teams will be equal to 15*2 = 30

8+6+5+5+4+F = 30

Therefore, points scored by team F = 2

F can either win 1 match and lose four matches, with zero draws.

Or F can lose three matches and draw two matches.

But no two teams can have zero draws.

So, F loses 3 matches and draws 2 matches.

The total points scored by F is equal to 2.