MyBB Community Forums

any way to make categories inside forum so that it may look in the way like the attachment

Read the MyBB documentation and wiki. It tells you all you need to know.

Yeah, just make a new forum, set it to be a Category, and choose the parent forum you want...

i have set it but it still shows this way..any suggestions

BTW why is it showing "forums contains new posts" instead of piture

I think you want this plugin:
http://mods.mybb.com/view/subforumsincolumns

And for the text, the image path must be wrong.

You can make a forum inside a category, but not a category inside a forum.
A category won't have a root, whereas a Forum would have a category as its root.
The image you showed in OP is of making sub-forums, and when you do it, you will get the look as shown in picture above.

And regarding the missing images, verify whether you have on, off and offlock images in theme image directory, and make sure, you have correct extension for images set in Forum bit templates.

You can have categories inside forums, you'll just need to have a forum inside that category.