${\left({\mathrm{CH}}_3\right)}_2\mathrm{Cd}$ is less nucleophilic than carbon. It can convert the acetic chloride into the acetone. The compound P is acetone. After that, acetone and acetaldehyde both have the alpha hydrogen. So, they give the cross-aldol and self aldol condensation reaction with sodium hydroxide and heat. The alkene can show the geometrical isomerism if there are different groups along the double bond.

Reaction :-

$$\begin{gathered} {\mathrm{CH}}_3\mathrm{COCl} \stackrel{\mathrm{i}) {\left({\mathrm{CH}}_3\right)}_2\mathrm{Cd}}{\to } \underset{\left(\mathrm{P}\right)}{{\mathrm{CH}}_3{\mathrm{COCH}}_3} \\ \underset{\left(\mathrm{P}\right)}{{\mathrm{CH}}_3{\mathrm{COCH}}_3} + {\mathrm{CH}}_3\mathrm{CHO} \stackrel{\mathrm{ii}) \mathrm{NaOH}(\mathrm{aq}.) ∆}{\to } {\left({\mathrm{CH}}_3\right)}_2\mathrm{C}=\mathrm{CH}-\mathrm{CHO} + {\left({\mathrm{CH}}_3\right)}_2\mathrm{C}=\mathrm{CH}-\mathrm{CO}-{\mathrm{CH}}_3 \\ + {\mathrm{CH}}_3\mathrm{CH}=\mathrm{CH}-\mathrm{CHO} + {\mathrm{CH}}_3\mathrm{CH}=\mathrm{CH}-\mathrm{CO}-{\mathrm{CH}}_3 \end{gathered}$$

Hence, the total number of products formed in the given reaction sequence is $4$.