You have fundamental lack of understanding about the process and terms.
DPI is dots per inch, and is a derived unit which requires dots and inches to calculate.
For computer images, inches have no meaning, they only exist in the physical world. For images you have dots only, and they are called pixels, which are irreducable. DPI is stored merely as a "flag" or "tag" and is honored or ignored at the whims of the software, much in the same way as a file name or the name of your dog.
If you have a "48x18 inch image at 72 dpi" that probably means you have an image which is 3456 pixels x 1296 pixels (48 inches times 72 dots per inch, 18 inches time 72 dots per inch).
The obvious implication here is that if you double the dimensions in inches, the dots per inch is halved. So in order to maintain the same dpi when enlarging an image, pixels must be manufactured and inserted. This always results in a loss in perceived quality.
You never need work with or manipulate DPI, you only work with pixels. You only need to think of DPI in terms of the equipment you are intending to output the image to, because that is the only time there will be inches involved at all.
Standard commercial CMYK printing has a rule of thumb of 300dpi, so one always tries to ensure that their 8x10 book cover image has at least 2400x3000 pixels. Billboards might be 30dpi so your 4x6 foot billboard would require a 1440x2160 pixels (yes, the billboard is actually a smaller image than the book cover).
To answer your question directly, "NO: changing the DPI does nothing for you. Provide the image AS-IS to you service provider and specify the final print size as 96x36 inches. If you can re-make the image with more pixels to start with (instead of scaling it), then do that but check with your service provider to see what their typical target DPI will be for that size print and use-case."
Note that this ignores vector-based art. If you have text etc, you probably don't want to send it as a simple image.