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The IUPAC name of the given structure is:
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A.${\text{3 - methyl - 3 - isopropyl hexane}}$
B.${\text{3 - isopropyl - 3 - methyl hexane}}$
C.${\text{3 - ethyl - 2,3 - dimethyl hexane}}$
D.${\text{2,3 - dimethyl - 3 - ethyl hexane}}$

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Answer
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Hint: IUPAC (International union of pure and applied chemistry) provides the names to organic compounds and the structures related to chemical sciences. It has some guidelines and rules to define the names for particular chemical structures.

Complete step by step answer:
In organic chemistry the naming of compounds is done on the basis of IUPAC nomenclature. IUPAC is also known as the International Union of Pure and Applied Chemistry. The naming of compounds ensures the uniqueness of compounds. Mostly it is useful for industrial purposes because IUPAC nomenclature does not create any confusion and also it is easy to explain to others what we are talking about. And from the name of compound we can easily depict the image of complex in our mind hence the naming concept for compounds is very useful.
Some basic steps are followed to derive the name of organic compounds, these steps are as follows:
Recognize the functional group present in the compound if any.
Find the longest carbon chain containing the main functional group.
Do numbering to the carbon atoms of the longest carbon chain starting from the nearest carbon atom of the functional group.
Check out the substituents or branched groups, do their naming separately with the same method as discussed in the above four steps.
Now it’s time to combine to combine all these things in one name.
So our organic compound is:
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The numbering of this compound will be done as follows:
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The maximum number of carbon atoms in the longest carbon chain of compound are six hence the suffix for the name will be hexane.
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As we can see in the above structure, substituents are isopropyl and methyl groups attached with the third carbon atom. This organic compound has not any functional group so we can write its name now with the help of numbering and the name of substituents only.
The naming will be done as: \[{\text{Prefix + name of substituents + Suffix}}\]
Therefore the IUPAC name of the given structure is ${\text{3 - isopropyl - 3 - methyl hexane}}$

Hence option (B) is correct.

Note: IUPAC is an international organization, basically it is a non – government organization which resolves the issues related to chemical science all over the world. The main motive of IUPAC is to encourage chemical science.