[GPhab]

1,1-dimethylcyclohexane   No stereoisomers
1,2-dimethylcyclohexane   (Cis,Trans)      Do 1,2- , 1,3- exhibit stereoisomerism?
1,3-dimethylcyclohexane   (Cis,Trans)
1,4-dimethylcyclohexane   (Cis-Achiral,Trans-Achiral)

Please justify your answer.

[GPhab]

Sorry. I meant to say do 1,2- ,1,3- exhibit enantiomerism

[Yggdrasil]

You are correct about 1,1-dimethylcyclohexane and 1,4-dimethylcyclohexane.  For 1,2- and, 1,3-dimethylcyclohexane you are also correct that there are cis and trans stereoisomers.  To see whether these are chiral, try drawing out either the cis or trans form, drawing the mirror image, and seeing if you can superpose the structures (if you can't do this visually, try building models).  Note that the answer may not be the same for both the cis and trans forms.