My first thought in response to SaamShams is (Paulenrique, Vivsaurus, DanMoller, please correct me!) when you say "as ### horas" you are refering to a specific time, as in, "six o'clock". As to having the article at all, I am a little confused, since in another lesson I think this same sentence was written as "Começou há seis horas", translated exactly the same way - "It started six hours ago." That makes me question mgaristova's comment below about "começar" requiring the "a" afterwards.
Hey bohle! No... it literally means "it started/began six hours behind", meaning "in the past"/"behind (us) now". Sounds weird in English, so please note that this literal example is only being used to illustrate a point, and I am not endorsing its use in everyday speech.
Also, "it started six hours late" would be "começou seis horas atrasado" (or atrasada). I hope it helps! =)