The hydrocarbon in 9a, 3-isobutylhexane, does not have the correct name since, when referring to the structure, the longest Carbon chain that may be generated from the structure should be called the parent chain.
Observe that in this instance, a 7 Carbon-Carbon chain can be formed in place of the typical 6 Carbon-Carbon chain to create an even longer chain. Therefore, heptane rather than hexane should be the parent chain.
Following that, take note of the methyl group linked to the third carbon and the ethyl group attached to the fourth carbon. The hydrocarbon's correct name should thus be 4-ethyl-2-methylheptane.

Since the name of the parent chain should correspond to the longest carbon chain that might be generated from the structure, the hydrocarbon in 9c(2-tert-butylpentane) has the wrong name.
Observe that in this instance, a 6 Carbon-Carbon chain can be formed in place of the 5 Carbon-Carbon chain to create an even longer chain. Hexane, not pentane, should therefore make up the parent chain.
Next, take note of the methyl groups that are connected to various carbons. The third carbon has one methyl group attached, and the second carbon has two methyl groups. Thus, 2, 2, 3-trimethylhexane should be used as the proper name for the hydrocarbon.
