During a holiday Mr. & Mrs. Harry went to a hill station named 'Wings

Split the days up into four categories:

1. Days when ONLY Mr. H walked
2. Days when ONLY Mrs. H walked
3. Days when they both walked
4. Days when neither walked

These categories don't overlap, and together, they make up the entire time that the Harrys spent at Wings of Lord. You want to know the entire length of time.

Statement 1: There were 8 mornings when both of them walked. So, there were 18-8=10 mornings when ONLY Mr. Harry walked, and 23-8=15 mornings when ONLY Mrs. Harry walked. We now know three of the four categories. However, we don't know the number of days when neither of them walked, so we can't find the answer. Insufficient.

Statement 2: There were 0 mornings when neither of them walked. We don't know the other categories, though - for instance, they could have never walked together, in which case they were there for 23+18 = 45 days. Or, they could have walked together on 18 days, in which case Mr. H never walked alone. Then, they would have been there for 23 days in total. Or, they could have been there for some other number of days in between the two.

Combined: Statement 1 tells you categories 1 through 3. Statement 2 tells you that category 4 = zero. So, we know all four categories - add them up to get the total number of days.