I want to print a 30" by 36" image at 4k is 72 good enough?
Those numbers are all related mathematically. You cannot just pick them at will.
"4k" is a 16:9 aspect ratio. 30"x36 is a 5:6 aspect ratio. If you force a 4k image to cover 30"x36", then yes the picture will have to be shrunk down in one direction (squares become rectangles, circles become ovals) to make it all fit. The things in the photo will look squashed, either skinny (squashed side-to-side) or fat (squashed top-to-bottom).
To print the 4k image at its original aspect ratio (squares stay square, circles stay circles), make sure "fit to page" is not selected when you print. On a 36" wide page, the math works out:
3840 pixels wide / 36 inches = 106.7 PPI
2160 pixels tall / 106.7 PPI = 20.24" tall
So if you print it at 106.7 PPI, the picture will cover the entire 36" width of the paper, but only span 20.24" of the 30" height. If it's centered on the page, there will be (30-20.24)/2 = 4.88" tall blank spaces above and below the picture.
If you print the 4k image at its original aspect ratio on a 30" wide page, then the math works out:
3840 pixels wide / 30 inches = 128 PPI
2160 pixels tall / 128 PPI = 16.88" tall
And the blank spaces above and below the picture will be (36 - 16.88)/2 = 9.56 inches tall.
Photoshop's resize command handles all of this seamlessly. You don't have to do any of the math.
■If you start with the 4k image and resize its dimensions (i.e. inches), it will auto-adjust the DPI to the correct value.
■If you start with the 4k image and resize its DPI, it will auto-adjust the dimensions to the correct value.
■If you hold the dimensions constant and set the DPI, it will resample the image to fit, either increasing or decreasing the number of pixels.
■If you hold the DPI constant and set the dimensions, it will again resample the image.
■If you hold the dimensions constant and tell Photoshop to change the picture size in pixels, it will adjust the DPI to match.
■If you hold the DPI constant and tell Photoshop to change the picture's size in pixels, it will adjust the dimensions to match.
(PPI is conceptually identical to DPI, it differs for esoteric reasons important to printer and monitor manufacturers. I can get into it if you want to know, but for most Photoshop purposes you can use the terms interchangeably.)
■For poster-size prints (36"x24") meant to be viewed from 5+ feet away, 72 PPI or better is usually good enough.
■For prints viewed from about 3 feet away, 150 PPI or better is usually good enough. This is typical for photos at gallery exhibitions.
■For prints viewed from 1-2 feet away, 300 PPI or better is recommended. This is typical for photos meant to be hand-held when viewed.