I think you are out of luck. One of the mods could delete posts, and entire threads, but they would need a very good reason to do so. Is there any reason you want to do this? Nancy's answer might be useful to another user with the same problem, so it is not 'clutter'.
Mark these forums are public on web servers that Adobe funds for their users to use and help each other out. Its open to all but only authorized moderators can remove threads or appends or close forums to make it read only. You may start a thread however you do not own the forum or thread their public. Data remains public it can be search and commented on.
The best you can do is mark your question as "answered" on the post that correctly answered it. That effectively tells others no further replies are necessary.
Keeping the discussions makes them searchable via Google and instead of posting the same question over, a user could look at your discussion and try the solutions there.
Don't worry too much about Adobe's disk space, there is plenty and they know what to prune and when to do it.
Discussions here are rarely locked by moderators. If you indicate which answer was correct, that puts a green balloon/check mark by the thread & usually ends further discussion. However, it may get resurrected later by another person with a related question. But this forum gets heavy activity so that isn't too common.