You can certainly output MP4s from Premiere Elements 8.
As I say in my books, in fact, there are many qualities, resolutions and compressions of MP4s you can create, depending on where you plan to display your video (on a disc, over the internet, on an iPod or iPhone, etc.).
Where do you plan to display your video and at what resolution?
My videos will be used for marketing purposes so it will be displayed on the Internet but it will be used for Padcasting and on mobile phones as well. The video I want to convert was recorded in HD.
You'll be best using these settings from John Cloudman.
To get to these settings, use Share/Personal Computer/MPEG with the H.264 preset, and then click the Advanced button to modify and create your own output preset based on John's above specs.