For a 24x36-inch print, 5400x3600 px is already about 150 ppi, which is generally good for a poster-sized print. At normal viewing distances, that’s usually sufficient.

You could go to around 7200x4800 px (about 200 ppi), but the visible improvement is usually small. In practice, many people won’t notice much difference, even on close inspection. Going all the way to 12000x8000 px for this print size is typically unnecessary.

For large prints, the final result depends not just on file resolution but also on the printer and print process. Printer quality, smooth tonal rendering, and the material used can matter as much as extra pixels. Some latex-based plotters, for example, can produce very smooth-looking prints.

So if your goal is a good-looking 24x36 poster at a reasonable cost, 5400x3600 is already a sensible target, and 7200x4800 is about as high as you’d likely need.