Above is a screenshot from my college's computer. He does have multiple inboxes in format of Tab bar.
See, He has switching/tabs like Classic, Important, Unread First etc.
Now, I request you to have a quick look at following snapshot from my machine.
I am just asking for enabling that kind of tabs in my Gmail.
Best Answer
Hover over inbox & click the dropdown arrow. Howevering over Inbox type lets you try out the tab-style UI for selecting Inbox type.