How many different stereoisomers are possible for the given molecule?

The molecule shown in the question possesses exactly two stereogenic (chiral) carbon atoms. A carbon is called stereogenic when it is attached to four different substituents, making interchange of any two of these groups generate a nonsuperimposable mirror image.

For a molecule that contains $$n$$ such independent stereogenic centres and has no element of internal symmetry (no plane or centre of symmetry that could make a meso form possible), the total number of stereoisomers is obtained from the formula
$$N = 2^{\,n}$$

Here, $$n = 2$$. Substituting, we get
$$N = 2^{\,2} = 4$$

Because the molecule lacks an internal mirror plane, none of these four configurations collapses into a meso (achiral) form. Hence all four are distinct: two enantiomeric pairs.

Therefore the molecule can exist in exactly four different stereoisomeric forms.

Option C which is: 4