The correct answer is $\boxed{\text{C}}$, tetra-9-naphthylethylene.
H2 addition is a reaction in which hydrogen gas is added to a double bond. This reaction is typically used to reduce double bonds to single bonds. In order for H2 addition to occur, the double bond must be in a position where the hydrogen atoms can approach the carbon atoms without steric hindrance.
In biphenyl ethylene, the double bond is located between two phenyl groups. The phenyl groups are large and bulky, so they sterically hinder the approach of the hydrogen atoms. This prevents H2 addition from occurring.
In tetraphenyl ethylene, the double bond is located between two phenyl groups and a hydrogen atom. The hydrogen atom is small enough to approach the carbon atoms without steric hindrance. This allows H2 addition to occur.
In tetra-9-naphthylethylene, the double bond is located between two naphthyl groups. The naphthyl groups are larger and bulkier than the phenyl groups, so they sterically hinder the approach of the hydrogen atoms even more than the phenyl groups do. This prevents H2 addition from occurring.