How to know the category ID of my categories?

On the Categories Panel, hover the mouse over the category name link and you will see the link address in your browser’s status bar (turn it on under View) or click the link. The last numbers in the link address is your category ID number.

It used to be clearly numbered in past versions of WordPress, but in current versions, it isn’t. That’s how you find it.

resolved, thanks a lot!

What Lorelle said is the easiest and fastest. Alternatively you can use get_the_category() and echo cat_ID and cat_name to determine what is what.

https://codex.www.ads-software.com/Template_Tags/get_the_category

where can i find the manage categories link in wordpress 2.7

See Administration > Posts > Categories

Also here’s a plugin that shows the IDs in the admin panel in a clearer fashion:
https://www.ads-software.com/extend/plugins/reveal-ids-for-wp-admin-25/