The plastic cover just hides the alternator belt, any oil leaking into the space behind the plastic cover can only be coming through the timing cover (the big plate on the front of the engine held on by all those screws)
The most likely problem is that the oil seal behind the alternator pulley has gone. The only other 2 possibilities I can think of are either the O ring seal behind the small square plate that covers the oil-pump/balancer shaft bearing (this sits in the timing cover) or the O ring that seals the ignition timing sensor on the very top of the timing cover.
You need to take off the plastic cover, it's only held on by about 5 screws and will come off in about 5 mins. You should then easily be able to see where the leak is.