Two Cubes Puzzle Solution

This puzzle is easy but you have to think out of the box to solve it.

We have two cubes so total 12 faces. So we can put 12 numbers on them. Since every month will have 11 and 22 so 1 and 2 should be kept on both the cubes. We have 10 number and 12 faces and we have to repeat two of them.

So it is simple. On 1st Cube:
The numbers will be 0,1,2,3,4,5
and on 2nd Cube we will have 1,2,6,7,8,9.

This looks fine but in the puzzle it is mentioned that the person uses both the cubes. So for date 4 it should be 04 but we cannot have it.So 0 should be kept on both the cubes. So then how we will arrange 13 numbers on 12 faces.

It's easy we can keep 6 on the cube and just turn it upside down to make it 9 whenever we want to use 9.
So the solution will be

1st Cube 0,1,2,3,4,5
2nd Cube 0,1,2,6,7,8

So you can make any combinations of dates using these cubes.