I'm talking about Redeem a Code not register game. Registering a game and Redeeming a code are two different options in two different sections of the Sims 3 website.
Registering a game is a 20 alphanumeric code.
Redeeming a special code is a 16 alphanumeric code.
If you go to the Sims 3 Store, sign in like you normally would. Then click on My Account at the top. You'll have to put in your password again usually. There should be a list of options under Account Details. This list is for the Sims 3 Store.
The list looks like this:
Choose Redeem a Code and it should have four boxes for the 16 digits. If your code is a only 12 digits, this may explain why a lot of people don't have to input the code to get access to the pet store in their purchase history. EA messed up and forgot to send out full codes and therefore, had to rig something.