Specifics are the key clue, however. Surely you can find at least one of almost every file format you can think of. There are web sites that can provide the hundred or more that are around. But we use only a very small sub-set of those and I've already mentioned nine of them. You can quote my previous post and simply add the app that opens it.
The dialog asking for an app to open a file it has lost connection with while suggesting you seek an app at the App Store is perfectly normal in this situation.
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Preview image files are opening in PS CS6... the ones like .jpg, .tif, .png, however .pdf files open in Preview
.jpg, .tif and .png files are not "Preview" files. Preview is mainly a PDF reader/writer. It can open and even export (even a pdf) to most image file formats. It does not have a built-in file type, although it usually assumes you want to save any file you open with it as the same format.
Image file formats are expected to open in an image editor like Adobe's apps or GraphicConverter.
There is a file in the system that keeps track of what suffix belongs to which app. There are third-party apps that can re-assign those matchings. It appears that the core file in the OS is corrupted and it needs to be replaced/repaired. I don't have time today to dig any further, but a search for something like "file type associations" might be of use. Please let us know what you find out.
You can also assign any file to be opened with just about any app by using its Info window.
