I would start be defining which which 1,4-dimethylcyclohexane I was starting with, or considering a mixture of cis and trans?
The tertiary carbons are most reactive as DrBob says, so there are two possible products from attack at the tertiary carbon:
cis and trans 1-chloro-1,4-dimethyl cyclohexane.
Attack at the secondary carbon adjacent to one of the methyl groups will result in 2-chloro-1,4-dimethylcyclohexane. If you start with a mixture of the cis and trans there are eight possible products which are:
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