He could be in a situation where he has to rely solely on his mental powers. Since he can't use his hands for combat or to perform certain Force - related physical actions, he might focus on telepathy or influencing the minds of his captors. For example, he could make them believe they see things that aren't there, causing confusion and creating an opportunity for escape.
Maybe he gets into a situation where he is bound and facing a Sith adversary. The Sith taunts him, thinking that Obi - Wan is powerless without the use of his hands. However, Obi - Wan uses his knowledge of the Force in a different way. He focuses on the energy around him, and starts to draw power from the life forms in the vicinity. This gives him the strength to break free from the bonds, or at least weaken them enough so that when the time is right, he can make a quick escape and engage in combat with the Sith.
Well, in a fanfiction, Obi - Wan with his hands bound could be part of a story where he is being held prisoner by a group that wants to learn the secrets of the Jedi. They think that by restraining him physically, they can break his will. But Obi - Wan, being a strong - willed Jedi, uses this time to meditate and strengthen his connection to the Force. He then starts to subtly manipulate the environment around him. Maybe he causes small objects to move in a way that seems natural, like a draft, but is actually his doing. This could be the start of his plan to not only escape but also expose the group's evil intentions.