I am looking to slay 12 webwood spiders. I am a alliance night elf but everytime I slay one it doesn't register

Make sure the spiders you are killing have their names above their heads in red lettering. Quest creatures will always have this feature. If the label is missing, you haven't targeted the correct spiders. I have come across a few quests like this in which it isn't completely clear what you are trying to kill. Look for the red label, and you will know you're on the right track. - LJS