Can you embed an image in Photoshop CS6 so that when you make a hyperlink the image will display on other computer screens, not just on my own? If so, how?
Images can not contain hyperlinks.
Hyperlinks are created by markup around an image, i.e. text.
For example, this would be a standard HTML link using an image:
<a href="mylink.html"><img src="myimage.jpg"></a>
The image is surrounded by markup (code) designed to perform some action.
Internally Photoshop doesn't really have any way to generate such markup merely by saving an image. It requires saving HTML and the image at a minimum.
You might take a look at Saving Slices with Photoshop from the Adobe Help Center.
Essentially, you need to build the construction around an image. You can't make the image itself link to anything.