Hello. I am new to Photoshop. I am taking photos of oil paintings with a Canon 90D camera. My original photos are 4640 px by 6960 px at 300 pixels/inch from the camera. I need to enlarge them to roughly 9000 px by 12000 px at 300 pixel/inch for a printing project. When I select "image size" and change the dimensions, I assume I am to keep the pixels/inch at 300 with resampling. Should I chose "Preserve Details (enlargement)" under the resampling tab? What percentage of noise reduction is recommended? Are there any other recommendations or better ways to enlarge my images (sharpening, other techniques, etc)? Thank you for your help.
You do not need to print a 30" br 40" image at a 300ppi resolution. Your 4640x6960 image printed at a 155ppi will print 30" x 45" and most likely be acceptable to you. Your image has a 2:3 aspect ratio not a 3:4 aspect ratio.
"I need to enlarge them to roughly 9000 px by 12000 px at 300 pixel/inch"
No you don't. "300 ppi" is the most persistent myth in the history of digital imaging. You don't need that for large format prints, that is, anything bigger than a book.
The bigger it is, the lower the ppi requirement, because it will be seen from farther away:
7000 x 4600 pixels is enough pixels to work for anything, from a book spread to a wall-sized banner - as long as the photo itself is of good quality (infinitely more important). Enlarging will never improve anything, it will only degrade the image. It will inevitably end up looking worse than if you had just left it alone.
The only justification for upsampling, ever, is to avoid visible pixels, which is not even remotely possible in this case.