Let's assume that Doo-Bee-Doo's age was N years when he died.
(life as a boy) + (life as a youth) + (life as a man) + (life as an old man) = (total life)
(N/4) + (N/3) + (N/5) + 52 = N
15N + 20N + 12N + 52*60 = 60N
13N = 52*60
N = 240 years
Thus, Doo-Bee-Doo was 240 years old, when he died. As he born in 1468 B.C., he died in (1468-240) 1228 B.C.