I'm sure that there's a better way but what I do is find what the 1:1 dimensions are of whatever I'm trying to print and then resize my image to be 1:6 the size of those real dimensions. For example, if a patch is 5" high, I will resize my image to be .833 inches high and then print it at the exact size of the resized image. Your image program should allow you to resize images by pixels or by print size. The print size option should also allow you to choose inches, centimeters or millimeters. When you print the image, make sure that you are printing it at 100% scale (that's the size of the resized image, not the size of the 1:1 image) and it should print out as an exact 1:6 replica of the original item. It sound more complicated than it actually is. You might want to try practicing by resizing and printing small images on regular paper using black ink rather than color ink. Good luck.
There isn't an easy way to do it because of the way printers and software interact with each other. I have had to paste multiple versions of the same thing on a page, each one a slightly different size, and print them all out. Then I measure each one and use the version that is closest to 1:6.
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