1. Understand the substrate

The given compound is

This is a cyanohydrin-containing ketone. The structure can be viewed as:

• The carbonyl carbon of the ketone is planar and can react with $\mathrm{HCN}$.
• The adjacent carbon $\mathrm{C(OH)(CN)Ph}$ is already a stereogenic center because it is attached to:
  • $\mathrm{OH}$
  • $\mathrm{CN}$
  • $\mathrm{Ph}$
  • $\mathrm{COPh}$

Since the compound is given as $(\pm)$, the reactant is a racemic mixture of two enantiomers.

2. What happens on addition of HCN?

HCN adds to the ketone carbonyl:

Now the former carbonyl carbon also becomes a stereogenic center because it gets:

• $\mathrm{OH}$
• $\mathrm{CN}$
• $\mathrm{Ph}$
• the adjacent substituted carbon

So in the product there are two stereocenters.

3. Maximum possible stereoisomers

With 2 stereocenters, the maximum number is:

These would normally be:

• $(R,R)$
• $(S,S)$
• $(R,S)$
• $(S,R)$

4. Check for meso possibility

The product has the general form:

Both stereocenters have the same set of substituents. Therefore, the $(R,S)$ and $(S,R)$ forms are actually the same meso form due to an internal plane of symmetry.

Hence, total distinct stereoisomers are:

• one meso form
• one pair of enantiomers

So total number of stereoisomers:

5. Effect of starting with a racemate

Since the starting material is $(\pm)$, both enantiomers are present and reaction at the planar carbonyl carbon gives all possible product stereoisomers. Distinct products remain the same count: 3.

6. Final answer

The derived answer matches the stored correct answer.