Here's the solution (I'm using the years 01 - 09 for simplicity):
Dates range from 20/02/01 to 31/01/09, just less than 8 years.
Here's my approach:
I took two dates which were just outside 6 months apart, 01/04 and 05/11. Incidentally, these and [20/02, 20/09] give the same overall result.
Then I looked for a date in September (19 months before April) and a date in June (19 months after November). So my list looked like [20/09, 01/04, 05/11, 19/06].
Once I had those filled in I only had to fit in February and January. I knew that if I put January in first then the total time would be >8 yrs, so February had to go at the beginning and January had to go at the end, giving the final list [20/02, 20/09, 01/04, 05/11, 19/06, 31/01].
Once I had all six dates in, I checked that they all fit in the 8-year period and were all at least 18 months apart, and pressed solve!