Six dice with upper faces erased are as shows.

The sum of the numbers of dots on the opposite face is 7.

If the odd numbered dice have even number of dots on their top faces, then what would be the total number of dots on the top faces of their dice?

Total 6 dices are given {I,II,III,IV,V,VI} 
A dice has {1,2,3,4,5,6} on their 6 distinct faces .

Condition I : Given that sum of opposite faces of dice is 7 .
Condition II : Odd numbered dices have even number on their top face.

lets use the logic of condition I and condition II :
I Dice : (3,4) & (6,1) are given , so the other pair has to be (2,5), And using condition II, now we can say Top face is 2.
II Dice : (5,2) & (4,3) are given, so the other pair has to be (1,6) .
III Dice : (6,1) & (4,3) are given, so the other pair has to be (2,5), And using condition II, we can say Top face is 2.
IV Dice : (2,5) & (4,3) are given, so the other pair has to be (1,6).
V Dice : (1,6) & (2,5) are given, so the other pair has to be (4,3), And using condition II, we can say Top face is 4.
VI Dice : (4,3) & (5,2) are given, so the other pair has to be (1,6).

Therefore, the sum of dots on odd numbered dices = 2+2+4 = 8.