If you like a tumblr image then put into your dropbox.
If
New like
This Trigger fires every time you like any public Tumblr post.
Then
Add file from URL
This Action will download a file at a given URL and add it to Dropbox at the path you specify. NOTE: 30 MB file size limit. Learn more
Discover more time saving integrations for Tumblr (legacy) and Dropbox