How many different IUPAC names can be assigned to hydroxy substituted benzene dicarbonitrile?

Hint: IUPAC nomenclature is the method of naming organic compounds by following standard rules given by the international union of pure and applied chemistry. The primary goal of the system is assigning each structure a unique and unambiguous name with which it can easily be identified.

Complete answer:
The compound given in the question is hydroxy substituted benzene dicarbonitrile, but the positions of each functional group is not mentioned clearly. So, according to the different positions of functional groups, we can assign different IUPAC names to the given compound.
The different structures of hydroxy substituted benzene dicarbonitrile along with their IUPAC name can be drawn as follows:
Structure-1:

The IUPAC name of the given structure is 2,4-dicyanophenol.
Structure-2:

The IUPAC name of the given structure is 2,3-dicyanophenol.
Structure-3:

The IUPAC name of the given structure is 2,6-dicyanophenol.
Structure-4:

The IUPAC name of the given structure is 3,5-dicyanophenol.
Structure-5:

The IUPAC name of the given structure is 3,4-dicyanophenol.
Hence, five different IUPAC names can be assigned to hydroxy substituted benzene dicarbonitrile.

Note:
The following points must be in mind before naming an aromatic compound:
When different groups are attached to an aromatic compound, then the numbering starts with the substituent of the base compound i.e., it is allocated first position (hydroxyl group in the given case).
The numbering of the carbon atoms in the ring should be done in such a manner that the value allocated to the functional groups is minimum.