I know how “easy” drag & drop is, but sometimes it is better to use the native commands on the device…in this case Linux on the MyCloud…learn some basic commands…
OpenTerminal app: ssh@mycloud
<password_for_mycloud> cd /shares/Public/old_directory (or where ever the files you want to move are located) mv *.jpg /shares/Public/new_directory (mv = move *.jpg = all jpgs)