It's hard to say without knowing how the website and homepage have been built unfortunately.
As a first step I would log into admin and go to CMS > Pages and find what looks to be the home page there and see if you can find the Shop Now links in there. The developers may reference static blocks (small reusable pieces of content) within the home page. In which case the "Shop Now" links could be in a static block in CMS > Static Blocks. Again, impossible for me to know what the static block might be called.
Thirdly, the developer may have used an extension to help build more complex content or sliders. So if you see anything referring to a slider in the admin interface then that would be a good place to check to.
Would you like to have a look in those places and see that helps at all?
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