Call Specific Categories Most Recent Image

Hey so I’m trying to create to featured images of different sizes set up next to each other at the top of my home page. I want each image to be the featured image from the most recent post of the respective given category. I can handle all of the stylist aspects just looking to know how I can call to the requested images in my index.php file.

I’ve read countless forum and blog posts as well as tried as many plug ins as I can find and I still haven’t hunted down the right approach.

Any help would be excellent, thanks in advanced.