Transparent background instead of white - Photoshop Elements 12

Nine or ten clicks to select the white areas and shadows (and maintain the white wheels), using the magic wand tool with the contiguous box checked:

I posted an example photo in one of my posts. It's not easy to do this with a magic wand

With respect to the shadows, you may need a higher tolerance to add to the selection, and/or make several clicks to add to the selection, but make sure that the Contiguous box is checked in order to separate the shadow from the product.

As Bob suggests, I recommend using the Magic Wand selection tool.  Use a fairly low tolerance level, and if it is a low resolution product image, turn off the Anti-aliasing box. 

Click on the white background to select it and then press the delete button.

Can you post an example image?

Try different levels of tolerance, but you will likely need to manually touch it up using another selection tool(s) and/or clone and healing tools.

Later versions of Photoshop Elements have better algorithms for that.