“…won’t let me”??? Do you mean it shows a message when you try to drag a folder to the trash and the item will not move to the trash? What is the message? Do you mean the item moves to the trash but when you try to empty the trash you get a message? What is that message? If you don’t tell us what exactly is happening, we have to spend a lot more time giving you solutions for three different possible problems.

First step:
Open a Finder window. Select the external drive on the left. Get Info. Check / tick the “Ignore ownership on this volume” at the bottom of the Get Info window. If that doesn’t help…

Second step:
Unlock all files in the problematic folder. Do this also in the Get Info window. Locked files cannot be removed from a drive.

Third step:
(for the issue can’t move folder to trash) Move one file at a time to the trash. When they are all in the trash, move the empty folder to the trash.
(for the issue can’t empty trash) Move one file at a time to the trash. Empty the trash after each move.

Forth step:
If the external drive has a name that includes spaces, rename it to remove the spaces (If the name is “backup disk”, rename it “backupdisk”).
Open Terminal. Follow the following steps exactly, and carefully note when I ask you to type a space or not.
Type:
cd /volumes
Press Return.
Type:
ls
Press Return. You will see listed (because ls means list) the name of the internal drive, such as Macintosh HD, and the name of the external drive.
Type:
cd externaldrivename

{Replace “externaldrivename” with the actual name of that drive.}

Press Return.
Type:
sudo rm -r .trashes
Press Return.
Now you see “password:”.
Carefully type your password even though you won’t see what you type.
Press return.
File > Quit.