I know this is a fairly basic question and people have asked about it before but I can't find the answer to my specific problem.
On Photoshop I make a new file with the size 4.188(w) x 1.75(L). I noticed immediately that it made my canvas size to 4.187 instead of 4.188. I figured it has to do with resolution. If I put it at 240 it will be the exact size I want but, since this is for printing I worry about the resolution being less than 300. Also, the people who want it require it to be 300. What the heck am I missing??
You may be confusing "resolution" and "DPI". Printers may request that the graphic be 300dpi (Dots Per Inch). So for example, a 4x6" print at 300dpi would have a "resolution" of 1200x1800 pixels (multiple dpi times inches desired for print).
If you wanted something printed at a 4x6" size, but only supplied the image at 1000x1500 pixels, that would be 250dpi and may not meet the minimum quality requirements of the printer.
The other possible issue is that they will print the image at 300dpi, and it will print out smaller than 4x6" as the source image is only at 250dpi - there's not enough dots to get a full-size print at 300dpi.