What we would typically do is remove the 4" solid surface backsplash - assuming it is not integral to the countertop. Then we would paint and install a tile backsplash all the way down to the countertop. Since you are leaving yours, you would need to select a tile that is not thicker that the existing backsplash and probably something that has no pattern so it won't clash.

Thanks so much for the information. Really appreciate it.

You can place an artistic mosaic backsplash
We can customize any picture to size and colors, or you can simply choose one of our designs from the website (www.mozaico.net)
http://www.houzz.com/projects/89358/Kitchen-Backsplash-Design-Ideas

I hope you'll find what you are looking for

The 4 inch extension is removed like Deborah Butler, Brickwood Builders said, and then you put in your backsplash tile