Problem source

I have two dice whose faces are all painted different colours. I number
the faces of one of them $1,2,2,3,3,6$ and the other $1,3,3,4,5,6.$
I can now throw a total of 3 in two different ways using the two number
$2$'s on the first die once each. Show that there are seven different
ways of throwing a total of 6. 

I now renumber the dice (again only using integers in the range 1
to 6) with the results shown in the following table 

\noindent \begin{center}
\begin{tabular}{llllllllllll}
Total shown by the two dice & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12\tabularnewline
Different ways of obtaining the total & 0 & 2 & 1 & 1 & 4 & 3 & 8 & 6 & 5 & 6 & 0\tabularnewline
\end{tabular}
\par\end{center}

Find how I have numbered the dice explaining your reasoning. 

{[}You will only get high marks if the examiner can follow your argument.{]}