My son has a cracked hose on his 2.4L Sonata. The hose comes out of the valve cover. Can anyone tell me what this hose is? And possibly the part number?

 

It appears to be part of the PCV system (Positive crankcase vent). It probably cracked due to heat exposure, which is not that unusual. You could most likely get a piece of the correct type hose from any auto supply store. You just need to make sure it is fuel and oil resistant, most auto supply stores sell it by the foot.and it would take just a few minutes to replace it.