Number of geometrical isomers possible for the given structure...

The isomerism that arises when atoms or groups having different spatial arrangements are restricted to rotate around a bond or bonds in a molecule is called geometric isomerism. This restricted rotation mainly occurs in a carbon-carbon double bond.

The conditions to form geometrical isomers are-

1. restricted rotation (often involving a carbon-carbon double bond);
2. Presence of two different groups on the left-hand end of the double bond and two different groups on the right-hand end. It is not necessary to have similar kinds of groups or atoms at both ends.

In the given compound, the central double bond is not give geometrical isomerism as it contains the same group on carbon, where the terminal double bonds (two double bonds) are exhibiting geometrical isomerism. Hence, the total number of isomers is ${2}^{2} = 4$ isomers.

Hence, the given compound shows four geometrical isomers.