"Printing" is the visual appearance of your genitals outlined by your panties. The term is one I first heard in reference to conceal/carry of firearms where your firearm 'prints' or is visible or obvious in some fashion through your clothes.
As for getting your genitals to fit in a thong, get one with a wider front band and learn to tuck your testicals up into the space behind your penis. Look into some videos on tucking for crossdressing or transwoman tucking. You don't necessarily need to go full tape style tuck, but once you get your testicles tucked up inside (it's where they go when your scrotum tightens up really tight when you're cold), and tuck your penis down between your legs, the thong should hold everything nicely.
Because I still have a bit of a pooch that folds down from when I was north of 300lbs (I've lost almost half that in the last 4 years), I don't wear thongs yet. I tend towards full coverage, or high-waisted panties and the tangas I mentioned above. Hipster briefs, very silky lacey boyshorts or high-waisted, low cut legged panties.
I have a couple of sport/shaper thongs with waist 4inch extra strong wist bands that I wear under some form-fitting outfits so they don't show panty-lines and they're wide enough in the front to keep things secure and tucked since they're designed to slim and shape.
It's taken a few years to find all of the different designs and shapes that are comfortable and look good on me as a well are pretty in their own right, but it was worth the effort. Experimentation is the key. Once this covid crap is cleared up and getting things from China is possible again, go hit aliexpress and spend $20-30 on a dozen or more pair of panties of different styles and sizes to find the ones that work for you.
Tabby.