File exporting PNG much larger than artboard size.

png options- Screen (72 ppi), Anti-aliasing Art Optimized (Supersampling).

If you are exporting an image 1080x1080 Px at 72 PPI, result will be 1080x1080 Pixels, but if you export the similar image with 300 PPI, dimensions of end result will be 4501x4500 Pixels. 

Group the content you wanted and export them from the assets pannel as PNG..

it worked for me.

To add to what everyone else is saying:

I've created an .ai file with the pixel dimension of 6075 x 4875 (20" x 16").

By @Jolynn5E1B

If you created an AI file with those pixel dimensions, it would be 84" x 68", not 20" x 16".

If you have a desired physical size/PPI, work from that -- not the pixel dimensions.

If your goal is to create a document 6075 x 4875, and you are in pixel measurement units, you need to export as 72ppi to give you a file that pixel size. Ignore the 72ppi... it's irrelevant here as it's the amount of pixels that's important for print. If it concerns you, simply open the image in Photoshop and change the resolution in Image > Image Size size to 300ppi without Resampling checked, and resave. Your file will still be 6075 x 4875, nothing has changed at all except the resolution flag that's in the header of the file.

Changing the ppi to 72 (Even though that won't work for my overall resolution because I'm printing a physical product.)

By @Jolynn5E1B

I don't understand that argument. If the pixel dimensions for the print should be 6075 x 4875 pixels and you deliver exactly that, the resolution of your file is irrelevant. It's just metadata.

For print work do not, repeat NOT set a design size in pixels. This works only when resolution is 72 ppi, because AI doesn't actually work in pixels at all; it thinks a pixel is a point (1/72 in). 

So, work out the required design size in inches (or mm) and work from there. Then, exported raster graphics should have more or less the expected size in pixels. 

Raster image export from Illustrator is doable, but short on control.

If you have Photoshop:

1. In Illustrator, Save a copy of the Illustrator file as PDF.
2. In Photoshop, set up a new, blank canvas at exactly the size and resolution required for your output.
3. Choose File > Place Embedded and select the PDF.
4. Scale and position the content appropriately, then tap the Enter key.
5. Save As... png