Twelve GB isn't too massive for an Outlook:Mac 2011 database. Personally, my Outlook database at work is 20GB.
Make sure that your colleague isn't running out of disk space. Outlook can have issues if there isn't sufficient hard disk space. My rule of thumb is that I should always have a bare minimum of 10% of my disk free. I'll also assume that you're up-to-date with both OS and Outlook updates.
If your colleague's Outlook content is exclusively stored in Exchange, an easy potential solution is to start afresh:
- Create a new user on their Mac.
- Launch Outlook.
- Enter their Exchange credentials.
- Let Outlook download everything from Exchange.
Since your colleague's account is so large, I would start this on a wired connection at the end of the day. If all goes well, everything will be downloaded by the following morning, and you can see if Outlook still has the same issues.
This will also work if your colleague's Outlook content is exclusively stored in IMAP/CalDAV/CardDAV. It won't work if your colleague has local content or if they are using POP.
If your colleague's Outlook content isn't exclusively stored in Exchange, try the following options:
There are some additional Outlook database troubleshooting steps available in the (unofficial) Office for Mac Help site. You could also try asking your question on the Outlook:Mac forums or the Mac Enterprise mailing list. If you do post to another forum, you should include some additional information in your post, like OS version, Outlook version, and the email server that you're using.
After you have resolved this issue, it might be worthwhile to see if you can archive some mail. If your colleague only needs to retain the emails in case they're needed, but doesn't actually refer to them very frequently, you could archive them. I've seen a few different methods for this, such as creating an Identity per year. This is outside the scope of your original question, so if this is something you're interested in, you can open another question and I'll answer there.