I'm not sure about this, but I would say 1,1,2,6,6,12,36,36,72,216,216,432
2 is formed from the sum of the two before it. Every number in a place that is a multiple of 3 i.e. 2,12, and 72, is multiplied by three. That number is then repeated and the sum taken. It seems strange, but it works for what you have given.
It makes no more sense than 77, 323, 967.
Please note that this problem is worded badly.
"What are the next three numbers in this pattern of 6 numbers?"
There are infinitely many possibilities. If you come up with one that you can justify, and you lose marks, you should go argue this point.
For the record, it is easy to justify 1,1,2,6,6,12,-2,-2,-2.
An infinite conclusion with finite information simply is not a reasonable request. It should say something like this:
"Add three numbers to this pattern of 6 numbers and justify your result."