He was elected to the Amtrak board because he rode trains a lot. From The Washington Free Beacon:
FLASHBACK: Hunter Biden’s One Qualification for Amtrak Board Was Taking Trains
Hunter Biden's only qualification for obtaining a seat on the Amtrak board of directors in 2006 was that he often rode trains.
That's according to his father Joe Biden's Delaware colleague in the Senate, Tom Carper, who offered the sole nomination speech for the younger Biden when his name was presented in the Senate Commerce Committee. In his prepared remarks, Carper said Biden would be an "excellent addition" to the board, but was unable to list any reason beyond his frequent use of trains.
"More significantly, Hunter has spent a lot of time on Amtrak trains," Carper said after listing schools Biden attended. "Like his father, Rep. Mike Castle and myself, Hunter Biden has lived in Delaware while using Amtrak to commute to his job in Washington, D.C."
Must be nice...