"When this episode happened I do not think I can have been less than twelve years old."
First, it's COULD not CAN.
Second, it's an awkward sentence construction. It's better to say: I think I could not have been... than I don't think I can have been...
The meaning is what Kate Bunting said: "he cannot remember his exact age at the time, but thinks he must have been at least twelve."
To make the meaning easier to grasp, just remove unnecessary words. Example:
"When that happened, I could not have been less than twelve."