Number of stereo isomers = $2^{\mathrm{n}}$

Where, $\mathrm{n}=$number of stereo centre.

The carbon atom which is attached with four different groups or atoms is known as stereo centre. The $2-$Bromo$-3-$chlorobutane has the two stereo centre. These are represented by the *.

So, the number of stereo centre $=\mathrm{n}=2$.

So, the number of stereo isomers =$2^2=4$

Hence, the number of optical isomers possible for $2-$Bromo $3-$Chlorobutane are $4$.