- 08/20/2020 (American)
- 20/08/2020 (everywhere else, as far as I know)
- 20/08/20 (quite common)
- August 20th 2020 (very common)
- August the 20th 2020 (also common)
- 20th August 2020 (quite common)
- 20th of August 2020 (also quite common)
It's a stylistic choice. On forms or in emails I would usually use the shorthand dd/mm/yyyy, personally. On the top of a letter I would use the longer version, but in the top of an invoice I might use the shorthand.
It depends on my mood, the style of the writing I'm doing, any style guide that I'm adhering to, etc.