Why does the combination fn+⌘+delete doesn't work?

Solution 1:

I don't know why it gives that shortcut, but try control-k.

See https://support.apple.com/en-au/HT201236

Solution 2:

"delete" in this article refers to the backspace key (← or ⌫) not the actual delete key (⌦).

So the combination your are searching for is ⌘ fn ⌫ or alternatively (if your keyboard has a number pad) ⌘ ⌦.

Note however that although these are system wide key commands, there are some 3rd-party applications that don't support them.

EDIT: The article also got some combinations wrong. It's ⌥ ⌫ for deleting the last word and ⌥ ⌦ or ⌥ fn ⌫ for deleting the next.

EDIT2:

It seems like ⌘ ⌦ and ⌘ fn ⌫ AREN'T system wide key commands (if that is a thing). They don't work in TextEdit or Pages BUT they do work in some other applications such as Apple's Xcode or TextWrangler.

Nonetheless you can achieve the same behaviour by using ⌘ ⇧ → (left arrow key) to select the text to the end of the line and then deleting it. This also works for words with ⌥ instead and for single characters with only ⇧.