File size shrunk from 22bm to 3.8 in lightroom with no cropping

>> My DNG file is 22 mb but in lightroom, the pixel size is only 3360x2240...

This does not compute. 3360x2240 is only 7.5 MP. An uncompressed 14 bit Raw/DNG would be 12.5 MB, but DNGs are compressed. I have old, archived 8 MP DNG files that are 6 MB and 21 MP files that make for 20-24 MB DNGs, while 24 MPs are about 26-30 MB. Maybe you have the original Raws embedded in the DNGs which would around double their sizes.

If part of the problem is a change in pixel dimensions, where no cropping has occurred, is there the possibility that you are dealing with Smart Previews instead of the original images or that some mobile upload/download is involved?

OK. Your pictures show that you exported as JPEG, so that explains everything. The entire point of JPEG is to crunch an image down to a smaller size. It does this by trying to throw out as much non-visible image data as possible (which limits future editing).

Be aware that you made an unconscious choice to use the DNG file size (22MB) as your reference. But 22MB is only the file size when that image is in raw (DNG) format and unedited. You must expect the file size to change, up or down, depending on what is done with the file, which features you used, and which format you used.

For example, the file size should increase beyond 22MB as soon as you save it in Photoshop or TIFF format, because of reasons such as bit depth and number of channels. The file size should increase again as you add layers and masks, if you switch to a higher bit depth, or a color mode with more channels, etc. When you're done editing, the file size won't change if you leave it in Photoshop or TIFF format, but will go down in a copy you export in a highly compressed format like JPEG.

There is no "true" file size for an image, but you can see the current uncompressed file size in Image > Image Size. Which probably won't match the current size on your desktop because of all of the variables already listed and more.

Sounds like you export as jpeg. JPEG is a highly (and 'lossy') compressed format, that is why JPEG files can be much smaller than DNG files, even if they have the same number of pixels.

 In finder, the file size is 22 MB. When I export from Lightroom with no cropping and no resizing whatsoever, it shows up back in finder at 3.2 MB. 

Where do you see 3.8MB? In the program, or after export to a different format that might be compressed?

Post a screen shot thanks!! Its a visual world of yours and mine . . .