The correct IUPAC name of the following compound is: 4 - methyl - 3 - ethylhexane 3 - Ethyl - 4 - methyl hexane 3, 4 - ethylmethylhexane 4 - ethyl - 3 - methylhexane

Rules for nomenclature:
i) Pick up the longest carbon chain.
ii) Start numbering from the nearest branch.
iii) In case two branches are at same distance from the terminal carbon, the branch having higher molecular weight is on priority.
In this case, the longest chain is with six carbons, the closest carbon with the branch is 3rd carbon. The next carbon with branch is 4th carbon.
Hence the the correct IUPAC name of the following compound is 3 - Ethyl - 4 - methyl hexane.
Hence, option B is correct.