I think the problem should say
My greatest digit is a 9, but I'm less than 900. I'm one more than a multiple of 10 and the sum of my digits is 12. Who am I?
If you are less than 900 then the 9 can't be the leftmost digit (the hundreds digit). Either the tens digit or the units digit is 9.
How can you tell if a number is divisible by 10? What does a number look like if it is one more than a number which is divisible by 10?