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The compound given to me is 1,2,3,6-tetramethyl cyclohex-1,4-diene.
The geometrical isomers for the following compounds are:

1,2,3,6-tetramethyl cyclohex-1,4-diene

The isomer on the right can also be an optical isomer with its enantiomer. So does this mean that there are 3 stereoisomers in total with one common geometrical and optical isomer?

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Your analysis is in right track. Yet, I would like to point some few points on deciding stereoisomers. The step by step analysis is depicted in following diagram:

1,2,3,6-tetramethyl cyclohex-1,4-diene isomers

The two geometrical isomers are $3,6$-$syn$- and $3,6$-$anti$-isomers. The compound has 2 chiral centers, hence $2^2 = 4$ maximum stereoisomers possible. However, as shown in the diagram, $3,6$-$syn$-isomer has a plane of symmetry. Therefore, its mirror immage is the same as indicated by $(3S,6R)$- or $(3R,6S)$-. In addition, $3,6$-$anti$-isomer does not has a plane of symmetry, and hence, has two enantiomers (see the diagram).

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    $\begingroup$ I think syn and anti in the diagram should be switched. Differs from text. $\endgroup$
    – user55119
    Apr 28 '20 at 22:59
  • $\begingroup$ Yes, and thank you. Just a mental mistake. :-) $\endgroup$ Apr 28 '20 at 23:02
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    $\begingroup$ Thanks a lot for your better explanation and clearing my doubt. $\endgroup$
    – PSN03
    Apr 29 '20 at 7:40
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Given compound has 1 geometrical isomer having methyl groups at trans , given is cis.Given compound has 2 chiral centers, C3,C6. Given structure is meso.C6 has S, C3 has R configuration. There exist its optical isomers having both chiral centers either R or S configuration leading to 2 optical isomers. Both having S configuration is also the trans isomer of given structure. Total 2 optical, 2 geometrical isomers(cis +trans).

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    $\begingroup$ your answer is wrong. There are 2 geometrical isomers not just one. $\endgroup$
    – PSN03
    Apr 28 '20 at 9:56
  • $\begingroup$ 1 meant 1 structure other than you had given,cis. For language clarity I had edited other 1 to 2(cis+trans). $\endgroup$
    – Fish2003
    Apr 29 '20 at 1:18
  • $\begingroup$ There are two geometrical isomers, cia and trans, but three stereoisomers, RS, RR and SS $\endgroup$
    – user55119
    Apr 29 '20 at 1:36

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