How can I get my video card / VGA port to output sound?
I want to plug the red, white and yellow RCA plugs into my RCA monitor (it has built in speakers).
VGA is video only. I can't possibly think of any use for the pictured adapter, except possibly with some non-standard specialty equipment that sends signals on pins where they shouldn't be.
Video cards don't emit audio. Video cards and audio cards can combine their efforts and send everything to a HDMI port, but each looks after it's own media.
You most likely want this pair of cables: