Hey there!! 
What are consecutive numbers ? 
Consecutive numbers re the numbers which are preceded right by the side. 
Example :- 2 , 3 , 4 , 5 are consecutive numbers. 
... 16,17,18 are consecutive numbers. 
The sum of two consecutive odd integers is 44. 
Example of odd consecutive integers :- 
... 1 , 3 , 5 are consecutive integers 
Note that the difference is 2 between each numbers. 
Let's take the first number as 'x' 
Then, the second number would be 'x+2' 
We added two because the difference is 2 is between any consecutive integers. 
... x + x + 2 = 44 
... 2x + 2 = 44
... 2x = 42
... x = 21 
The first number is 21, addition of 2 is 23. 
Hence, the numbers are 21 and 23.
Hope it helps!!