Binomial probability function vs simple theory

Hmm, thinking about this logically, rather than mathematically -

roll #1 - one chance out of six to roll a six
roll #2 - one chance out of six to roll a six
etc.

Can also be put as -
roll #1 - five chances out of six to roll a non-six
roll #2 - same as above, etc.

We also care about there being 2 rolls of six, so the condition of one roll of six must be fulfilled, and then it has to be fulfilled a second time, but only a second time. E. g. if the first roll of six happens on roll #6, that's no good.

I don't know if this is helping, or if it's confusing (and I apologize if it's the latter). Haven't thought about straight logic problems in years; thanks for the opportunity to do so.