Illustrator is somewaht hardwired to the 72 ppi resolution. So you can only export a raster format of the desired pixel dimensions and then and then change its resolution in an image editor.
Or you do the math. Setup the document dimensions in a way that will convert to the desired pixel size when you output it in 300 ppi. But that might always gibe you rounding errors.
In Illustrator, set your artboard to the size the want. In your case, it's 930x310px. Apply a "holding line" to the artboard using the rectangle tool with no fill, no stroke and then lock it. Upon export, set the res to high ( 300ppi ). If you do not apply the holding line to the parameters of the artboard, the artwork is automatically clipped to the artwork, not the artboard. Try it and see what happens.
If they really mean that you need to keep the image at 930 pixels AND 300 PPI, you will have to scale it down to fit. 900 pixels correspond to 3 inches (900/300 = 3).
When going from 72 to 300 PPI, you should go from 930 to 3875 pixels, not 3879, so you may have a look to see whether your image is off the pixel grid.
Which exact requirements are you facing, if you can quote it here?
Edit: Hi Monika and John.