So, let's break this down.
There are two ways to die by hanging.
-You can drop from a height, snap your neck, severing your spinal cord, which paralyzes your diaphragm and intercostal muscles, greatly reducing your ability to breathe. That, along with constriction of the trachea, leads to a quick death.
-You can tie a noose (or something similar) around your neck, resulting in gradual asphyxiation. This leads to a slower death and a lot more struggling.
In order to break the hyoid bones, it would seem like you have to fall from some distance, to cause sudden pressure against the bones, but they could also be broken if someone wrapped something around your neck and crushed them (or crushed them with his hands).
I suppose it is possible that he tied one end of the sheet around his neck, and the other around the top of the bunk bed, while he was lying/crouched on top of the bed. He could then roll/crawl off the bed in an attempt to snap his neck, damaging the hyoid bone. But, his feet would have to hit the ground after the sheet pulled taught. If the feet hit first, it would greatly reduce the sudden pressure applied to the hyoid. The sheet would also have to not tear and the knots would have to be good enough that neither end suddenly gave slack.
TLDR: It might be possible for him to fracture the hyoid bone in a suicide attempt, but it would be a lot more likely that someone else was there and fractured it while choking him out (with hands or with the sheet wrapped around his neck).