Youtube used to show the list of all keywords used to tag a particular video in the description section but a few years back they stopped displaying this information. But you can still find these tags by viewing the HTML source of the video page and then checking out the Open Graph or OG tags. OG Tags are standardized markups that Youtube uses on all its videos. So let's see how this can be done.
Step 1: The first step is to open the video in your browser and then view the source of the video page. You can view the HTML source of a page by right clicking on a blank area and then left clicking on the 'view source' option (as shown in the image below) or by clicking CTRL + U on your keyboard. .
The following image shows you how to view the source in the Chrome browser but it is the same in all browsers. Some browsers use the term 'View Page Source' and some others use the term 'View Source'.
Step 2: On the HTML source page, search (CTRL + F) for the term 'og:video:tag'.
And there you have it, if the video author has used tags for his video, you will be able to see all the tags.
For example: Let's check for the tags used in the following video:
Video Title: How To Make A Forum In WordPress
Video URL: https://www.youtube.com/watch?v=6GGeE3P09sQ
When we view the source of the video and search for 'og:video:tag' we get the following:
Note that these tags are not auto-generated by Youtube but are custom tags inputted by the author of the video. So if the author does not use tags, then your search will not return any value.