Step 1: Formation of Grignard reagent.
Benzyl bromide (Ph-CH\(_2\)-Br) reacts with Mg in dry ether to form benzyl magnesium bromide:
\[
\text{Ph-CH}_2\text{-Br} + Mg \rightarrow \text{Ph-CH}_2\text{-MgBr}
\]
This is a Grignard reagent, which is highly reactive nucleophilic organomagnesium compound.
Step 2: Reaction with CdCl\(_2\).
Grignard reagent reacts with cadmium chloride (CdCl\(_2\)) in a transmetallation reaction. In this process, MgBr group is replaced by Cd to form organocadmium compound.
Step 3: Formation of dialkyl cadmium compound.
Since Cd is divalent, it bonds with two benzyl groups:
\[
2 \, \text{Ph-CH}_2\text{-MgBr} + CdCl_2 \rightarrow (\text{Ph-CH}_2)_2Cd + 2MgBrCl
\]
Step 4: Identify product structure.
The final product is dialkyl cadmium compound where two benzyl groups are attached to Cd:
\[
(\text{Ph-CH}_2)_2Cd
\]
Step 5: Reaction type understanding.
This is a classic organometallic exchange (transmetallation) where Grignard reagents convert into less reactive organocadmium compounds used in controlled synthesis.
Step 6: Final conclusion.
Thus, product P is benzyl cadmium compound with two benzyl groups attached to Cd.
Final Answer:
\[
\boxed{(\text{Ph-CH}_2)_2Cd}
\]