This might sound similar to Abambo’s great reply, but anyway…
72 ppi or 300 ppi have no meaning…until you lock them to a real world dimension such as inches. Then it means a lot. The big mistake a lot of people make is stating a ppi value without also stating the real world size (in inches or cm) they want to print the image.
The key to the whole thing is the simple equation:
Pixel per inch (ppi) = pixels / inches
Using your 4200 x 3000 image as an example:
4200 pixels divided by 72 ppi = 58.33 inches.
Therefore, sure, it’s a 72 ppi image…if you intend to print it 58.33 inches long! But you probably don’t, so 72 ppi is not useful here. Why does it say 72 ppi? The file might not have a ppi value in it, and in some applications, 72 ppi is just the default value the software plugs in when the file doesn’t have a ppi value. So, it’s not meaningful.
Let‘s work out what would be meaningful.
If you want to print it at 10 inches wide (as in a 10 x 8 print) then the effective resolution of the printed image would be:
4200 pixels divided by 10 inches = 420 pixels per inch.
If you want to print it 30 inches wide (as in a 30 x 20 inch gallery print) then the effective resolution is:
4200 pixels divided by 30 inches = 140 ppi.
As a 6 x 4 inch print for a snapshot album, the effective resolution is:
4200/6 = 700 ppi
So the ppi of the same 4200 x 3000 px image is not one single number. It’s different for each print size. The ppi is one of its pixel dimensions (4200 or 3000) divided by whatever the same dimension of your print size is. Accounting for the print dimension is what tells us whether it will be 140 ppi, 700 ppi, or something else.
If instead you plug the ppi into the equation and let the print dimension be the variable, then the equation tells you the usable print sizes of any image. By doing this, we find that if we want an image to have an effective resolution of no less than 300 ppi, then:
The maximum print size of your 4200 x 3000 px image, at 300 ppi, is (4200/300) or 14 inches long.
The maximum print size of a 6000 x 4000 px image from my camera, at 300 ppi, is (6000/300) or 20 inches long.
Since you asked about actual print quality, you can account for viewing distance. In my 30 x 20 inch print example, it will be large enough that it will usually be viewed from further away than a small print, so a lower print ppi is OK because it will seem like more ppi from a further distance. So if a file for a 30 x 20 inch print works out to 150 ppi, that might be OK depending on your expected viewing distance.
So in the end, your file is not 72 ppi period.
It’s 72 ppi at 58.33 inches long.
and
It’s 300 ppi at 14 inches long.
and
It’s 700 ppi at 6 inches long.
etc.