Take a look at the link below which shows a method using the find command about half way down the page.
find Downloads -type f \( -iname "*.pdf" -o -iname "*.png" -o -iname "*.txt" \) > files.txt
The code above is run from /home/user, you need to put the actual path to your directory where you see Downloads above. It will then output a list of files with the extensions .pdf, .png and .txt to a files.txt file in the directory from which you ran the command. You will need to make the appropriate changes to fit your needs.