a. The compound `(A)` contains two asymmetric `C` atoms with the same terminal group.
Number of optically active isomers `(O.I.A)= 2^(n-1)=2^(2-1)=2`
(where `n` is the number of asymmetric `C` atoms).
Number of meso from`=2^((n-2)//2)=2^(0)-1`
Total optical isomers `=2+1=3`
Due to one double bond, the number of geometrical isomers `=2`
The number of stereoisomers `=3xx2=6`
b. If the stereochemistry about `(C=C)` bond is `cis`, then two pairs of diastereomers (II) and (III) are possible.
(II) is meso `(O.I.A)` due ot the presence of plane of symmerty . (III) is optically active `(O.A)` and two enantiomers are possible. Therefore, in total there are three diastereomers.
II and `(+) III, II` and `(-)III` are diastereomers, wheras `(+)III` and `(-)III` are enantiomers.
c. If the stereochemistry about `(C=C)` bond is trans, two pairs of diastereomers (IV) and (V) are possible. (IV) is meso `(O.I.A)`, due to the presence of centre of symmerty. (V) is `O.A` and two enantiomers are possible. Therefore, the in total there are three diastereomers.
[`IV` and `(+)V]` and `(-)V`] are diastereomers, whereas `(+V)` and `(-V)` are enantiomers.
d. Therefore, the total number of diastereomers from (b) and (c ) is six.