So, part of the problem you may be having is that DPI or PPI (dots per inch/pixels per inch) is a variable setting that can be changed when making or resizing a digital canvas. Your DPI is what determines how many pixels equal an inch on your canvas. And every program starts with its own default DPI set. For example, in Photoshop, when you create a new file, starts the DPI at 72, meaning 72x72 pixels will equal 1x1 inches. This is something you can manually change based on your needs. The higher your DPI, the higher the overall resolution will be, creating a crisper, but bulkier file. A lower DPI means a smaller, but not very high-def image, so to speak. When creating a new file in your program, when it lets you set the height and width, it should also have a resolution/dpi/pixels per inch box with some present number in it, usually 72, 150, or 300.
My recommendation for creating web-based images is to start with a higher dpi, like 300. I start my images even higher, usually, like 500 or 600, but that's not always necessary. Once you have the image the way you like, your program should let you resize your canvas, and you can make the image smaller, more web-friendly. 72 dpi is fairly standard, but quite small. This is all based on what kind of fidelity/file-size you want out of your image. Your client may have an idea of how large or small the file should be.
(I never recommend working smaller and scaling up-- your image will become large and blurry.)
If you're dead-set on using inches, just by copy-pasting in the provided measurements in pixels, then switching the units over to inches, the program should automatically convert this over for you. When I tried this, the conversion came to 6.333" w x 4.0" h. When changing your dpi, these units won't change, since it's simply changing how many pixels will fit into an inch.
Hope this is helpful!