There are 36 possible rolls and only one is a double 6, so the
probability of one double 6 in 1 roll is 1/36.
on your TI-84 
press 2ND VARS
Scroll down to binompdf(, press ENTER
Don't get binompdf( and binomcdf mixed up, the "c" is for
"cumulative" and the "p" is for "particular value".  This is
a particular number of times, 2.
         trials:20
         p:1/36
         x value:2
         Paste 
Press ENTER
binompdf(20,1/36,2)
Press ENTER
.0882934291
Edwin