I have a 10x High Def. 2 element macro lens, which was purchased for an older Kodak EasyShare Z612 camera. Since it now appears that the camera may be broken beyond repair, I need to know if there is some other camera that this lens will work with. The lens also says: "Digital NC 58 mm Japan Optics" and Bower.
The lens also says: "Digital NC 58 mm Japan Optics" and Bower.
It sounds like the macro lens you have is actually an auxiliary lens that attaches to the front of the camera's main lens. If that's the case, then that lens will probably attach to any other camera with the same diameter and thread pitch. From the 58mm in your description, it's a good bet that the diameter is 58mm, and filter thread pitches are pretty well standardized, so it should fit most cameras or lenses that takes a 58mm diameter filter.
The "lens" you have is a type of teleconverter that screws onto the 58mm filter threads of real lenses. It will fit any lens that can use 58mm filters, either directly or via step-up or step-down rings.
If you get a real interchangeable lens camera to replace your broken camera, you will be able to use real lenses that fit your needs without teleconverter filters. If you still want to use the teleconverter filter, it should work with most kit lenses (18-55/3.5-5.6, 55-250/4-5.6), which often have 58mm filter threads.
It's the question what a 10x lens is. Closeup lenses are measured in dioptres and don't actually cause significant magnification (I assume that a 2 element 1 group lens is what you have, the typical achromatic closeup lens construction). Instead they change the range where a camera can focus, allowing you to use the zoom capacities of your cameras from quite closer. Is this really marked/marketed as 10x rather than +10 ? On this camera, "tele zoom" reaches to a distance of 0.6m so an actual 10x lens would reach to 0.06m, making for something like +15 dioptres. Which seems unusually strong and would be almost impossible to handle regarding depth of field.
At any rate, it sounds like you have a standard thread of 58mm. A whole lot of cameras have threaded filter mounts (and you shouldn't really buy one without since you lose a lot of versatility) and if you don't have 58mm on your new camera, adapter rings are rather cheap. Closeup lenses make most sense when you have a tele-capable lens/setting that cannot focus in close range. If your tele focal length aperture is comparably fast and your closeup lens diameter is smaller than your objective's filter thread, you may have to stop down somewhat to avoid loss of sharpness and contrast. But you usually want to do that anyway with a strong closeup lens since otherwise depth of field becomes unmanageable.
Each camera/lens maker specifies the type of mount. For example Canon has EF and EF-S mount, Nikon has F mount and so on. There are certain lens mount adaptors which make incompatible lens and camera combinations to work. You can search accordingly.