If abba is divisible by 4 and 9 it will be divisible by 36.
A number is divisible by 9 if the sum of its digits is divisible by 9, so 2a+2b=2(a+b) is divisible by 9.
A number is divisible by 4 if 4 divides into the 2-digit number ba.
If 2(a+b) is divisible by 9 then a+b must be a multiple of 9: 09, 18, 27, 36, 45, 54, 63, 72, 81.
Eliminate those not divisible by 4 leaving 36 and 72 only.
So abba can be 6336 and 2772. Their sum is 9108.