In the U.S., this is a children's expression for a large number. In this story, the children are obviously very young and can't add 3+3. At this age, children might count 1, 2, 3, 4, 5, 6, 7, leventy-leven.

"eleventy-eleven" made no sense to me, so I had to 'google' it. Apparently, it's a US regional expression that means a very large number. How widely (or not) it's used, I have no idea, maybe those from the US can help ?

It's hard to know without more context, but I think it's a joke isn't it? It's gibberish, like twelvety. I could well be wrong and Greg's answer of the regional term might be correct. It reads, to me, as a joke wherein two young kids, or idiots, are 'making up' names for numbers. ... and yes, the actual answer is six :)