Let the digits be these 4 blanks to fill in:
_ _ _ _
>>...The sum of my hundreds digit and my tens digit is 15...<<
The only pairs of digits that have sum 15 are {6,9} and {7,8}
>>...My hundreds digit is one less than my tens digit...<<
Therefore the pair is {7,8} so the number is
_ 7 8 _
>>...The sum of my thousands digit and my ones digit is 5...<<
The only pairs of digits that have sum 5 are {0,5}, {1,4} and {2,3}.
>>...my ones digit is one more than my thousands digit...<<
Therefore the pair is {2,3} so the number is
2 7 8 3
Edwin