First, although your title mentions touch, the command you have actually used is mkdir so you have created a directory called new_file. You will not be able to write text to new_file as-is.
In fact there's no need to create the target file in a separate step: redirecting a command's standard output to a named file will create it automatically if it does not already exist. You can remove the (empty) new_file directory using rmdir ~/Desktop/new_file
For the reasons outlined here Why is printf better than echo? you might want to consider instead using
printf 'Hello\nworld\n' > ~/Desktop/new_file
or use a here document
cat > ~/Desktop/new_file
Hello
world
which allows you to enter multiline text directly, terminating the input with Ctrl+D when you're done.
In either case, you can replace > by >> if you want to append to, rather than overwrite the existing contents of, the file.