For the given reaction:

'P' is

The correct answer is cyclohexanecarboxylic acid (represented by the chemical formula:
$C_6{H}_{11}-\mathrm{COOH}$).

Step-by-Step Explanation:

1. Identify the Reactant:
The starting material shown in the first image is 1,2-dicyclohexylethene, where a central carbon-carbon double bond ($C=C$) is flanked by two cyclohexyl ring substituents. The chemical structure is:
$C_6{H}_{11}-\mathrm{CH}=\mathrm{CH}-C_6{H}_{11}$

2. Analyze the Reaction Conditions:
The reagent indicated above the reaction arrow is potassium permanganate in an acidic medium (${\mathrm{KMnO}}_4/H^{+}$). Under these strong acidic and oxidizing conditions, alkenes undergo oxidative cleavage.

3. Mechanism of Oxidative Cleavage:
During oxidative cleavage with acidic ${\mathrm{KMnO}}_4$, the carbon-carbon double bond is completely broken:
- Alkene carbons that are monosubstituted (bonded to one hydrogen, like $-\mathrm{CH}=$) are oxidized to carboxylic acids ($-\mathrm{COOH}$).
- Alkene carbons that are disubstituted (bonded to no hydrogens) would be oxidized to ketones ($-C=O$).

4. Determine the Product 'P':
Since both carbons of the double bond in our reactant are monosubstituted, the double bond is cleaved to form two identical carboxylic acid molecules:
$C_6{H}_{11}-\mathrm{CH}=\mathrm{CH}-C_6{H}_{11}+4\left[O\right]\to 2C_6{H}_{11}-\mathrm{COOH}$

Thus, the major product 'P' is cyclohexanecarboxylic acid, which consists of a cyclohexyl ring directly attached to a carboxylic acid group ($-\mathrm{COOH}$).