I would like to know if I can write a post to promote a free online webinar about database training in this Database Administrator community.
Please note that the point of asking a question is to ask a question. The goal is not to write posts.
I'm pretty sure using the question functionality to promote your webinar is going to get the post deleted quickly.
There isn't any strict rule against mentioning it when it's relevant to an actual question or answer, but posting just for the sake of advertising isn't according to the guidelines and scope.
As Michael pointed out, there is an ad system for that, either community sponsored ads or actual paying for an ad.
There's this, but it's mostly about link-only answers.
There is (were?) community promotion ads. You could claim a stake in that if appropriate.
For my two cents - posting a question or answer as advertising is likely to get short shrift. Chat's fine. All sorts of things get discussed there. It gets fewer views than the main question list, of course.