Get embeded video from a post and display it elsewhere

First of all, I’m newbie. Secondly, I searched all the web and everything I found was this. It’s exactly what I need but it didn’t work for me, I tried but I got an error (Fatal error: Cannot redeclare show_thumb().)

So basically, there’s a slider on my homepage which shows the lastest post from each category (the category name, the post title and the featured image on each slide). Each slide is a li item inside an ul.

If the post has a video embeded, or has the category “Video”, I want to get the video embeded (instead of the image) and put it on this slider behind the content – and get something like:

<ul>
<li>
<h2>Title</h2>
<h3>Category</h3>
<object>
</li>
</ul>

This slider is only at index.php.

– This is the printscreen of what I have now
– This is what I want (kind of)

I hope you’ll understand.
Thank you very much!