Right now your image at 72 dpi is 21.4" wide by 16" tall. If you convert to 300 dpi without resampling (the only way to keep the image quality), it would be 5.1" wide by 3.9" tall. If you convert to 300 dpi and resample the image, it will look like Mario did in Donkey Kong if you were to print it at full size.
The problem with starting out with a 72 dpi image is that it has to be huge to get to 300 dpi and still have an image that is a good size for printing on a garment. Typically stuff you find on the internet is not big enough to convert. You only have so many pixels in a raster (bitmap) image. You can't grow more by changing the dpi. There is the finite amount of pixels, and all you can do is spread them in tighter or loser groups per inch. The larger the spread, the worse it looks at larger print sizes.
Your image has about 1.8 million pixels in it. To print large prints, like on garments, you need raster images with around 20 million or more pixels in them. They need to start life with that many pixels because, like I said, you can't grow more. With some expensive software like onOne's Perfect Resize, you can fake grow more pixels with good results.
One thing to note, vector images are not pixel dependent, they can be scaled up or down and then converted to 300 dpi raster images for printing. If you start out with a raster image, you need to start at 300 dpi full printing size. If you work with vector images you don't have a size problem to worry about.
The problem with starting out with a 72 dpi image is that it has to be huge to get to 300 dpi and still have an image that is a good size for printing on a garment. Typically stuff you find on the internet is not big enough to convert. You only have so many pixels in a raster (bitmap) image. You can't grow more by changing the dpi. There is the finite amount of pixels, and all you can do is spread them in tighter or loser groups per inch. The larger the spread, the worse it looks at larger print sizes.
Your image has about 1.8 million pixels in it. To print large prints, like on garments, you need raster images with around 20 million or more pixels in them. They need to start life with that many pixels because, like I said, you can't grow more. With some expensive software like onOne's Perfect Resize, you can fake grow more pixels with good results.
One thing to note, vector images are not pixel dependent, they can be scaled up or down and then converted to 300 dpi raster images for printing. If you start out with a raster image, you need to start at 300 dpi full printing size. If you work with vector images you don't have a size problem to worry about.