You can fly, take a train, take a bus, or drive from Barcelona to Valencia. Go to the related link and fill in the blanks. They will recommend a driving route if that was what you wished to know.
Driving distance is 351 km - about 3 hours 25 minutes per Google Maps. According to my route planner the distance is 365,3 km. and the driving time is 3 hours and 30 minutes. I bet they got stuck on...