this means that 9-a+b-c+2 is divisible by 11, so b-(a+c) is divisible by 11.
so this value is either -11 or 0.
if it is -11, we can use casework.
first take the case where b is 0.
the a can be 2, c can be 9, or a can be 3, and c can be 8, all the way up to the case where a is 9 and c is 2.
this has 8 possibilities.
now you take the case where b is 1. the sums are 12, and there are 7 posibilities using the same logic.
you keep doing this untill you get 1 possibility, so there are 8+7+6+5+...+1 possibilities or 28.
now if b-(a+c)=0, then it is the same.
if b is 0, there is one possibility.
if b is 1 there are 2 possibilities.
and you keep doing this until b is 9 and there are 10 possibilities.
this makes 1+2+3+...+10=55 possibilities for that case.
now you just add them up and get 55+28=83 possibilities.
HOPE THIS HELPED!!