Number of geometrical isomers?
Geometrical isomers refers to isomerism in which the connectivity of atoms is preserved, and changes refer only to the spatial arrangement of the atoms. In other words, it only allows transformations around certain features that can be arranged in different ways in three dimensions (and which aren't just conformers that will easily transform into each other due to molecular motion).

I mention this because your reference to a "cycloalkene [...] having [8 or more] carbon atoms" suggest that you are looking for constitutional isomers (i.e. compounds with the same atoms but different connectivity) and not just geometrical isomers (i.e. compounds with the same connectivity but different spatial arrangement).

If we consider geometrical isomers of the compound you gave, 1) the cycloalkene ring, 2) the side chains and 3) the substitution sites in the ring are fixed (as changing them would produce constitutional isomers), so we are left with isomerism due to cis/trans double bonds.

You have three double bonds in the side chains that will produce $2^3=8$ isomers. Cyclooctenes are in principle large enough rings that their trans form can be isolated, so this leads to $16$ isomers; you can figure them out from your posted example (which is cis in the cycloalkene and trans in the side chains) by changing double bonds.

If you want to figure out constitutional isomers, that's a far more complex task; you'll have to account for ring size, number of side chains, ring substitution pattern, branching, position of insaturations and so on; with a hydrocarbon of this size, the number of possibilities will be huge.