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I identified the orange portion as the longest carbon chain which is the first step.
Next, I can't call it 3-ethylhexane as the bromine is a branch from a methyl branch.
This is the problem I am facing. Since the methyl branch is on the 3rd carbon, and bromine branch is in the "branched" 2nd.
So, is it called as 3-(2-bromomethylhexane)? Or have I got it wrong?
3-(bromomethyl)hexane
You can't have a 2-position on a methyl group, there is only a 1-position and we omit redundant 1-enumerations of position.
This type of formulae can be confusing. Might be helpful to redraw it as $$\ce{CH3(CH2)2CH(CH2CH3)CH2Br}$$ or $$\ce{CH3CH2CH2CH(CH2Br)CH2CH3}$$ There is only one carbon atom in methyl, so 2-bromomethyl is nonsense. The locant means on which carbon atom is the functional group attached. There exists a type of nomenclature, where the locants designate the position, where the carbon atom was replaced, it would be theoretically 2-bromaethyl, but it is never used for halogen compounds; sometimes is for compounds containing oxygen, nitrogen, ... (oxa-, aza-, ...).
When there is only one possibility where to place the the substituent, it is possible to exclude the locant, so 1-bromomethyl becomes just bromomethyl.
The composed substituent name must be in parentheses so the final name is 3-(bromomethyl)hexane, as Lighthart has answered. Without them, there might be confusion whether it might mean (though not completely defined) 3-bromo(methylhexane).
UPDATE: Why the correct name is NOT 1-bromo-2-ethylpentane? There is no principal functional group with suffix, the name is composed using substitutive nomenclature, which is the preferred naming method for halogenated hydrogarbons. The principal chain is just the longest one. Bromo group then has no priority over alkyl substituent (besides alphabetic order).
The IUPAC name for this compound would be 3[ 1' - bromomethyl] - hexane
//Edit: Where 1' refers to the carbon in the methyl group attached to the 3rd carbon in the primary chain. Also if you had an ethyl group attached and if the Bromine was attached to the 1st or 2nd carbon in that chain then it would be 1' -bromoethyl.... And 2' -bromoethyl.... . Try drawing this structure of this compound.
3-[1'-bromo - 2'- chloro- 3' - flouro- 4' - [1"- methyl ethyl] hexyl] hex- 3 - ene.
Apply the same concept, i.e., the carbons in the longest chain of the substituent group will be numbered 1', 2', 3' and so on and the carbons in substituent group of the substituent group would be 1", 2", 3" and so on.
