Tablecloth layout on Illustrator

1. Ignore the pixel dimensions given

2. Ignore the "Full Bleed Size" given (seeing as it's the same as the Trim Size; you can' go wrong)

3. Set up a new artboard with the true dimensions given: 126.5 x 61.25

4. Create your design

That's all one can answer with the info you posted. I suspect you're then expected to upload something; most likely a raster image of 6325 px X 3063 px, which is only 50 ppi at the size given. Seems a bit low for something that will be less than 24 inches from the users' eyes.

Make a new document to the bleed size of 126.5" x 61.25".

Click and let go of rectnagle tool and enter 126.5" x 61.25".

Is strange that your bleed and trim, size is exactly the same, as your bleed should be larger. Bleed is the excess part of print trimmed off, and there to help with press misregistration to ensure the ink goes to the edge of print. You could contact wherever you got those values, as your trim size for example might actually need to be 126" x 60.75", for having .25: bleed.

Do not use  Ilustrators bleed settings.  Will be less confusing for you, and every printer will accept accept a file where the canvas size includes the bleed, and some will not get the bleed if you use do nto later check the correct settings.