The correct option is
B 3-ethyl-2,5,5-trimethylheptane
The longest continuous carbon chain in the molecule has 7 C atoms and this chain is called the parent/ main/principal chain.
The branched carbon atoms get the lowest possible number.
When chains of equal lengths are competing for selection then that chain is selected which has more number of substituents/branches. The chain numbered above has maximum number of substituents.
If the same substituent occurs more than once in the molecule, then prefix di (for two), tri (for three), tetra(for four) are used to indicate how many times it appears. Here , methyl group occurs thrice, so tri prefix is used
The naming of the substituents should be in alphabetical order.
The correct IUPAC name of the above compound is 3-ethyl-2,5,5-trimethylheptane