Export Original is one of the presets that comes pre-installed. But do you really want to send him a raw file (with edits in xmp)? I would start by asking him to specify his complaint.
Your 300 resolution setting is basically meaningless. The image is 2400 x 1832 pixels regardless of what the resolution is. It all depends on what your graphic designer needed to do with that image. Changing the resolution will do nothing to increase or decrease the quality of the image. The only thing that would change the quality would be to provide more pixels.
> He then complained that I sent him a low quality image.
I'm afraid he is right, in general terms that is a low resolution image. It is a 4 Megapixel image and modern cameras output images that are much higher in resolution - 20 to 50 Mp. So unless your camera is more than 15 years old, it is probably capable of much more. It sounds as though you are downsizing the image at export and if you can show us a screen shot of your Export Settings, perhaps we can help.
On the other hand, if all you want is a 6x8 print or to share it online, a reduced size image of those dimensions is entirely adequate for that. But you would not need a graphic designer for that.
I would note, however, that for a 6x8 print the image dimensions should be 1800x2400 pixels and since the printer will crop it to that you may lose some important details from the short side. Adjust your crop in LR to be an aspect ratio of 3:4.
He then complained that I sent him a low quality image.
So then ask him specifically to provide details about what is low quality.