Guest I think you may have misread the question.
(unless it was me of course)
Find the number of 3-digit numbers, where any two adjacent digits differ by 1.
Let the first digit by 2,3,4,5,6, or 7
Then there will be 6*2*2=24 such numbers
Say the first digit is 1 or 8
101
121
123
898
878
876
there are 6 of those
Say the first digit is 9
987
989
there are 2 of those
So that is 24+6+2=32