Then why do I visit other wordpress blogs and under the posting is a "Like This" with pictures?
As raincoaster and I have told you, it's only when viewing posts individually.
If you're still not convinced, kindly show us an example of another WordPress.com blog where you see that.
I just checked on my husband's computer and my blog does not have the top bar that has the follow, "like" star, reblog.
That bar appears only whenever one is logged into WordPress.com and visiting another WordPress.com blog. In other words, if I were to go on your blog right now, I'd see it.
On your husband's computer, if you go to http://wordpress.com, sign in, and THEN go back to your blog, you'll see the bar you are talking about.
That STILL won't change the fact that you cannot "Like" a post from the homepage. You have to be viewing that post individually in order to "Like" it.