Is there a way to see the DPI of an image you hae opened in illustrator? I have an image open but it doesn't show in the document info window any resolution
Also checked linked and it shows the PPI but not the DPI
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Digtal images don't tenchnically have a DPI setting (they have pixels, not dots)*. It doesn't matter what the PPI is set at either - I see it's set at 72ppi in your screenshot, but this means nothing really. DPI is the print output resolution. It's not the resolution of the image. It really only comes into play when printing, or when preparing documents for printing.
Taking your example, an image at size 3024*4032px printed at 300dpi will be 10.08" x 13.44". All you need to do is divide each dimension by 300 to work it out. If you print at 600dpi instead then the it will print at 5.04" x 6.72". So, the DPI depends on the size you want to print it at, and the number of pixels the image contains.
You can also do this in reverse: first decide what size you want it to print at, and divide the pixel dimensions by the physical dimensions in inches to work out the DPI.
*Note that graphic design software such as Photoshop, InDesign, Illustrator, etc, often uses PPI as an equivalent to DPI for the purpose of placing images at the correct size, although technically they aren't really the same (dots are not equivalent to pixels). But for all intents and purposes, PPI is used as though it were equivalent to DPI. So if you set your image to 300ppi (without resampling), and place it into InDesign or other similar software, the image will be placed at the size calculated above.
See The Myth of DPI for more detailed information, an old but still very useful article.