The reaction \[{C_{12}}{H_{26}} \to {C_6}{H_{12}} + {C_6}{H_{14}}\] represents:

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In the above reaction given, the reactant is broken down into two simpler organic compounds.

Complete step by step answer:
In order to find the type of reaction the given reaction is, let us first discuss the different options given to us:
-Substitution reaction: a particular reaction is said to be a substitution reaction if one of the functional groups of the reactants is substituted by another functional group. Substitution reactions are also known as single displacement reactions.
-Synthesis reaction: Synthesis reactions are basically when there is a direct combination of the reactants, that are simple in nature, to form relatively complex compounds.
-Cracking reaction: Cracking reactions are those reactions when complex organic compounds get broken down into relatively simpler organic compounds.
-Polymerisation reaction: In this type of a reaction, the monomer/monomers of the desired polymer are made to react under certain conditions. This leads to attaching of the monomers in the desired order and at the desired locations to form the desired polymer.
After understanding the above descriptions and observing the reaction at hand, we can say that a complex organic compound, i.e. \[{C_{12}}{H_{26}}\] breaks down into 2 simpler organic compounds.
Hence the reaction \[{C_{12}}{H_{26}} \to {C_6}{H_{12}} + {C_6}{H_{14}}\] represents cracking.

Hence, Option C is the correct option.

Cracking reactions are mainly and widely used in the petrochemical industries where the crude sources might be longer, more complex organic compounds, while the desired products might be a lot simpler in nature.